Students immediately check their work by finding their answer in the next box. endstream endobj 1283 0 obj <>/Encoding<>>>>> endobj 3 0 obj <> endobj 4 0 obj <>/Type/Page>> endobj 26 0 obj <>/Type/Page>> endobj 39 0 obj <>/Type/Page>> endobj 52 0 obj <>/Type/Page>> endobj 61 0 obj <>/Type/Page>> endobj 73 0 obj <>/Type/Page>> endobj 74 0 obj <>stream B,. Solve: \(- \frac { 1 } { 2 } ( 10 x - 2 ) + 3 = 7 ( 1 - 2 x )\). Solving equations and inequality worksheets is helpful as they are used to compare numbers and decide the range or ranges of values that fulfill the circumstances of a given variable. +3.q >P4xAW.F8F;q?qRT*P Equations and inequalities can be represented on a number line. Worksheet by Kuta Software LLC. This BUNDLE does not include ALL items within this Unit, but only the items with a solving Systems of Equations &a, Do your students need a refresher on equations, inequalities and linear functions in general? This is done by using letters to represent unknowns, restating problems in the form of equations, and by offering systematic techniques for solving those equations. Click here to check your answer 3. Inequalities typically have infinitely many solutions. | Algebra 1 & 2, Setting Up Solving and Graphing Linear Equations and Inequalities Review, Solving Systems of Linear Equations and Inequalities - Complete Lesson Slides, Solving Linear Systems of Equations and Inequalities Station Activity, Solving Systems of Linear Equations and Inequalities Complete Worksheets, Solving Systems of Linear Equations and Inequalities Algebra Unit, Algebra 1/Math 1 Curriculum Bundle-Algebra Lessons with PowerPoint/Google Slides. The questions include simple questions to find the value of a variable and can move on to tougher graphical or word problems. For example: \[\begin{align*}10 &> - 5 \\[4pt] Clear fractions by multiplying both sides of an equation by the least common multiple of all the denominators. This unit is a bundle of these concepts and will require very little time for the teacher to prepare since everything is provided for you. Linear Equations and Inequalities Worksheets | Download Free PDFs - Cuemath hq: LT%ald-BMi?Huk'y6Sj;%&6fp7ht-h+NVnH 7*WXB85G&cYVa\BdM+Rfd8AE@iv}_/A$Lm+@ q\g}|b! Before you get started, take this prerequisite quiz. I w, Double-sided "cheat sheet" or reference page over solving equations and inequalitiesSteps to solve equationsHow to graph inequalities No Solution Vs. Infinite Solutions, No prep and ready to print, these guided notes will help your students learn how to solve linear equations and inequalities. !L:i66|}KR5 MwJ68wZa:(9kJcQJ+z=w?CuZwLgj :q._2-fc1WN^bT$cSP[WZO\f9+ PDF Linear equations and inequalities in one variable - City University of In this text we will choose to present answers using interval notation. When solving linear equations, the goal is to determine what value, if any, will produce a true statement when substituted in the original equation. Linear equations and inequalities worksheets give kids an idea of how to solve linear equations and find the answers to inequalities. -8 = -16 + n. Worksheet by Kuta Software LLC. 1235 0 obj <>stream \(\begin{aligned} - 7 y - 3 & = 11 \quad\color{Cerulean}{Add\: 3\: to\: both\: sides.} PDF Solving Two-Step Inequalities Worksheet Reasoning with equations and inequalities worksheet - Math Methods To understand why we included the parentheses in the set up, you must study the structure of the following two sentences and their translations: The key was to focus on the phrase twice the sum, this prompted us to group the sum within parentheses and then multiply by \(2\). Solving inequalities with fractions worksheets aim at teaching the students how to deal with inequalities in fractions. I use this as a study guide for STAAR and as a review for students if they have to retest in class over this unit. 18pt Linear equations worksheets including simplifying, graphing, evaluating and solving systems of linear equations. Solve linear equations and linear inequalities in one variable, including equations with coefficients represented by letters (literal that are linear in the variables being solved for). Solve linear inequalities and express the solutions graphically on a number line and in interval notation. Step 5: Finally, answer the question in sentence form and make sure it makes sense (check it). Web students can practice problems by downloading the linear equations worksheets in pdf format for free.Web h uk7uit2a8 fsooufxtcwuaoraeh rlvl5ck.i 1 fa4lwlq fryipgmhltwsl mrbelsyeir5vield7.p 9 km0a8dkek wwyiqtchp giynefyilnhilt 3er larlfgze5bqrla2. Guided student notes for Intermediate AlgebraTeacher notes (student notes with answers)Presentations in Keynote for Apple Products and PDFExamples are from the OpenStax free courseware textbook. Linear equation: 2= 3+ 1 \(\begin{array} { r } { 5 ( \color{Cerulean}{- 4}\color{Black}{ )} + 7 < 22 } \\ { - 20 + 7 < 22 } \\ { - 13 < 22 } \:\:\color{Cerulean}{} \end{array}\), \(\begin{array} { c } { 5 ( \color{Cerulean}{6} \color{Black}{)} + 7 < 22 } \\ { 30 + 7 < 22 } \\ { 37 < 22 } \:\:\color{red}{} \end{array}\), \(x=4\) is a solution and \(x=6\) is not. Linear Equations and Inequalities Worksheet PDF. Simplified Ratios Word Problem Worksheet 1 - With this 10 problem worksheet, you will practice writing and simplifying simple ratios while looking at how ratios are used in real-life. \(\begin{array} { r } { \{ x | x < 3 \} } &\color{Cerulean}{Set\: notation} \\ { ( - \infty , 3 ) } &\color{Cerulean}{Interval\: notation} \end{array}\). A1M9pR}E+a*Y{5 S${1E|1/EJxkGE9ojgLNYlm&N*n&4[ 8V Alternatively, we can multiply both sides of \(a=2\) by negative one and achieve the same result. Multi Step Inequalities Modeling Teaching Resources | TPT Related topics you might like: Writing &, Power Point includes animated step-by-step instructions for creating a foldable for either "Solving Linear Equations" and "Solving Linear Inequalities." Slope. Graphing systems of linear inequalities worksheet answer key - Math ]c~Ono9xxQ(V6 Tv>h M=NqMJyy]j #K~?-K#!WSJgm8Q })4Y!N),LD;{&oC(5J&ed'-3NRR.9)dWD.rpfg hK\~ . \(\begin{aligned} 5 ( 3 - a ) - 2 ( 5 - 2 a ) & = 3 \\ 15 - 5 a - 10 + 4 a & = 3 \\ 5 - a & = 3 \\ - a & = - 2 \end{aligned}\). Typically linear equations are not given in standard form, and so solving them requires additional steps. We use the left parenthesis symbol, (, to show that the endpoint of the inequality is not included. MC. 1. Linear Inequalities Application Problems.pdf So let's see, we wanna be greater than or equal to 4$, we're gonna spend $1.20 on orange juice and then the amount that we spend on donuts . Printable in convenient PDF format. 1.2 Notes: Solving Linear Equations. Use this packet to practice necessary basic math operations to be successful on the TSI or ACCUPLACER. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. Equations and inequalities may be represented on a quantity line. These math worksheets should be practiced regularly and are free to download in PDF formats. If you're looking for a fun way to teach your kids math, try Decide math. 2011-10-03T14:46:12-04:00 =nt>?|aNkN&_x#>%&PJZ7!>)hw>#L>W>Jn ? Are \(x=4\) and \(x=6\) solutions to \(5x+7<22\)? We can also represent inequalities using interval notation. Pre-made digital activities. . 16pt 1) a number increased by 5. 3 0 obj SECTION 3.1: LINEAR EQUATIONS A. 34 total questions. The Textbook Exercise on Solving Inequalities. 20 questions that get progressively more difficult as the students work through the circuit. 130An equation that can be written in the standard form \(ax + b = 0\), where \(a\) and \(b\) are real numbers and \(a 0\). 5p < -25 19. Do not try to clear fractions when simplifying expressions. Solve each inequality. 8 = 16 + n 3. 1161 0 obj <> endobj Therefore, we begin by subtracting \(8\) on both sides of the equal sign. 15 - 5k 0 14. TPT empowers educators to teach at their best. PDF Linear Equations - College Algebra Section 2.1 - Math 1310 Each lesson contains a PowerPoint to display while students are taking notes on the PDF that is provided. You can also use them individually.- Final answer key is included in the worksheet when applicable for self-assessment.- Manageable number of questions and graduate level of difficulty.- Complete solution file is included for the teacher. When this is the case it is possible to use the multiplication property of equality to clear the fractional coefficients and obtain integer coefficients in a single step. Mathematical foldables (or gr 1184 0 obj <>/Filter/FlateDecode/ID[<9D126D529814A74B9CAAD449527FF8DB><0A0F665A7A87EB43B68CD8BCE126640B>]/Index[1161 75]/Info 1160 0 R/Length 113/Prev 319934/Root 1162 0 R/Size 1236/Type/XRef/W[1 3 1]>>stream 5 x - 11 -14 18. Sheila J. Waggoner and Jennifer A. Marsala Solve Linear Inequalities Worksheet. Distribute and multiply all terms by the LCD to obtain an equivalent equation with integer coefficients. CHAPTER 2 Solving Equations and Inequalities 84 University of Houston Department of Mathematics Additional Example 2: Solution: Additional Example 3: Solution: We first multiply both sides of the equation by 12 to clear the equation of fractions. Solving Literal Equations Solving Simultaneous Equations Simultaneous equations are introduced and examples are done to show how two different variables are solved for simultaneously in a linear and a quadratic equation. The barcode scanner beeped as I passed it over the items in my cart. We then shade in all the numbers to the left of one, to show that all numbers less than one are solutions (Figure \(\PageIndex{3}\)). To get the worksheet in html format, push the button "View in browser" or "Make html worksheet". It is important to know that this technique only works for equations. 19 = b 6 2. Graph your solution. Solving Multi-Step Equations Translating algebraic phrases in words to algebraic expressions Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. Dividing by \(0\) is undefined and multiplying both sides by \(0\) results in the equation \(0 = 0\). Customize the worksheets to include one-step 583 Math Teachers 11 Years in business 83695+ Completed orders Get Homework Help Complete the Property Table - Level 1 The boundary lines in this set of graphing two-variable linear inequalities worksheets are in the slope-intercept form. Simplified Ratios Word Problem Worksheet 1 PDF. -4k - 5 3 23. \(\begin{aligned} - 4 a + 2 - a & = - 4 \left( \color{OliveGreen}{\frac { 1 } { 5 }} \right) + 2 - \color{OliveGreen}{\frac { 1 } { 5 }} \\ & = - \frac { 4 } { 5 } + \frac { 2 } { 1 } \cdot \color{Cerulean}{\frac { 5 } { 5 }}\color{Black}{ -} \frac { 1 } { 5 } \\ & = \frac { - 4 + 10 + 1 } { 5 } \\ & = \frac { 5 } { 5 } = 1 \:\:\color{Cerulean}{} \end{aligned}\). 24pt x-intercepts and y-intercepts. There are seven parts, and each section has a "Things to Remember" box with hints about that particular topic. VERIFYING SOLUTIONS A linear equation is made up of two expressions that are equal to each other. If given fractional coefficients, then multiply both sides of the equation by the least common multiple of the denominators (LCD). \\ 9 x = 3 & \quad\color{Cerulean} { Solve. } Solving Linear Equations And Inequalities Worksheets & Teaching These math worksheets should be practiced regularly and are free to download in PDF formats. Skill Summary. worksheet solving inequalities algebra kuta graphing systems software In this case, it is the \(LCD (3, 5) = 15\). The solution set is the intersection of the individual solution sets for an "and" inequality. The goal is to obtain the variable term on one side of the equation and the constant term on the other. 1. Let's start owith a very, very simple example. In other words, think of this as \(56 = +8 + 12y\). Solve and graph the solution set: \(2(4x5)<92(x2)\). The step by step method is very good for learning and understanding the problem, i use it when my teacher is not available for help with math hw. 30 -30 - 6x 13. The following are some examples of linear inequalities, all of which are solved in this section: A solution to a linear inequality139 is a real number that will produce a true statement when substituted for the variable. The preview shows various types of questions included. This awesome series of worksheets and independent lessons for students will help you learn how to solve inequalities or linear equations that have a single. + 17 > 4 24. . A linear equation may have one or two variables in it, where each variable is raised to the power of 1. This step not only makes our work more readable, but also forces us to think about what we are looking for. Solving Inequalities Worksheet Pdf - Template and Worksheet Example 4.2.1 (A very, very simple example). the method/s of solving quadratic inequalities. Graphing linear equations and inequalities worksheet | Math Index Inequalities Worksheets - Math Worksheets 4 Kids Algebra 1 worksheets systems of equations and inequalities graphing linear with answer key worksheet printable solving math exercises problems free 2 for homeschoolers students pas teachers concept 12 Algebra 1 Worksheets Systems Of Equations And Inequalities Graphing Linear Inequalities Worksheets With Answer Key Inequalities Algebra 1 Worksheet Printable Worksheets Solving Equations Math . Shade to the left of 2.5 and put a parenthesis at 2.5. Download Linear Equations and Inequalities Worksheet PDFs These math worksheets should be practiced regularly and are free to download in PDF formats. Linear equations and inequalities worksheet | Math Guide Write each as an algebraic expression. Customize the worksheets using the generator below. 56 CHAPTER 4. l]H3m\D,!U -7y < 21 21. Solving linear equations packet - Math Index Evaluate 6x 4 when x = 2. . "U:4&x$Ls i a @ p8-T089;r9B an2 < )~sh9F\Y) LINEAR STATEMENTS IN ONE VARIABLE 4.2 Solving linear equations in one variable In this section, our goal will be to develop a method that will "nd" all the solutions for certain equations in one variable. Border: Bordercolor: redmagentabluepurpletealgreenorangegrayblack. This has the advantage that you can save the worksheet directly from your browser (choose File Save) and then edit it in Word or other word processing program. The worksheets suit pre-algebra and algebra 1 courses (grades 6-9). Writing and solving linear functions equations and inequalities kuta Get math help online . application/pdf Solve: x = 2. Shade to the left of \(\frac{3}{5}\), and put a bracket at \(\frac{3}{5}\). \\ { x > - \frac { 1 } { 2 } } \end{array}\). Solving equations and inequality worksheets is helpful as they are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable. :S5c][Tjevq.nmjZ-ve#rB(k;GVXNUibL"Oa}ensDA#28iN6LW\/fWK1\lB6;Nv,]mZM 137An equation that is never true and has no solution. -9 + x . endobj Solve and graph the solution set: \(\frac{1}{2}x2\frac{1}{2}(\frac{7}{4}x9)+1\). Linear equations are used in several data and computer science applications. \(\left. The notation for inequalities on a number line and in interval notation use the same symbols to express the endpoints of intervals. x7VlD(`DFN' )pcm/Nz_l%xq :.TTRY{ c/ HRl"I"6vt@@McT_DIG^`f51Nw*. As students answer the questions, they will reveal the letters that help them solve the riddle. 7 < 4q - 9 \\ - 5 x + 4 = 7 - 14 x & \quad\color{Cerulean} { Combine\: opposite-side\: like\: terms. } You can generate the worksheets either in html or PDF format both are easy to print. (72) $2.50. This is the step by step solutions they should be getting in school ,but us often rushed and not available. 1) . ]ReSSC{S59S)&FP#2q^z oihhf5Nk)VNtm;lv5>4h, Sheila J. Waggoner and Jennifer A. Marsala, College Algebra, University of Houston Department of Mathematics. 3 3 x > -4 15.-2x - 14 86 16. Solving Linear Equations Worksheet Pdf. This item contains:*** 14 word problems, variable on either side*** Multiple choice of inequalities modeling each situation*** Blank space for showing work*** Students will select the inequality that . Use algebra to solve the resulting equations. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 3 < 2 x + 1 9.-8x + 18 > -22 10. To illustrate the problem, consider the true statement \(10 > 5\) and divide both sides by \(5\). 2: Solving Linear Equations and Inequalities - Mathematics LibreTexts Solving equations & inequalities | Algebra 1 | Math | Khan Academy uuid:5fb60f1c-dbb1-4dbe-8301-0c423d0816ca \(\begin{aligned} 56 \color{Cerulean}{- 8} & = 8 + 12 y \color{Cerulean}{- 8} \\ 48 & = 12 y \\ \frac { 48 } { \color{Cerulean}{12} } & = \frac { 12 y } { \color{Cerulean}{12} } \\ 4 & = y \end{aligned}\). Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Algebra simplifies the process of solving real-world problems. by. Let's do these together. For now, set up all of your equations using only one variable. General guidelines for setting up and solving word problems follow. 6 Complete lessons: This complete Google Slides lesson covers how to solve linear equations and inequalities at an Algebra 2 level. This section reviews the basic techniques used for solving linear equations with one variable. \\ 5 x + 3 & = 3 x - 15\quad\quad\quad\color{Cerulean}{Solve.} Included are the following:- Step by Step instructions for Solving Linear Equations from one-step to multi-step- Determining types of solutions in Linear Equations- Step by Step instructions for solving linear equations involving the distributive propertyThis is a resource your students will find helpful! Even though the College Ready Packets were meant to prepare students for college entrance exams, they can be useful for any secondary math class as review material. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. m solving equations packet.pdf Create printable worksheets for solving linear equations (pre-algebra or algebra 1), as PDF or html files. Normally this involves combining same-side like terms. If there are infinitely many solutions, we graph the solution set on a number line and/or express the solution using interval notation. Here we point out that \(a\) is equivalent to \(1a\); therefore, we choose to divide both sides of the equation by \(1\). -A.2C write given, Expressions, equations, inequalities and literal equations are key to success in Algebra and college readiness. A@@`&68@nDJi0, Write an equation for each line in Slope-Intercept Form. The left bracket symbol, [, would show that the endpoint is included. In interval notation, we express \(x>3\) as \((3,\infty)\). Step 3: Translate and set up an algebraic equation that models the problem. INEQUALITIES, NUMBER LINES, AND INTERVAL NOTATION. Using inequalities to solve problems Get 3 of 4 questions to level up! However, if you multiply both sides of an equation by \(6\), you obtain an equivalent equation. \\ 1x & = 3 \cdot ( - 2 ) \\ x & = - 6 \end{aligned}. Inequalities Word Problem Worksheet - Fontana Unified School District College Algebra, University of Houston Department of Mathematics Solve and graph the solution set: \(2(x+8)+620\). Step 2: Identify the variables by assigning a letter or expression to the unknown quantities. Solving quadratic equations By taking square roots By factoring With the quadratic formula By completing the square Radical Expression Simplifying radicals Adding and subtracting radical expressions Multiplying radicals Dividing radicals Using the distance formula Using the midpoint formula Solving radical equations Easy Hard Free Printable Algebra Worksheets for all Grades 16. x + 12 > -15 17. Horizontal & vertical lines. Next, isolate the variable using the equality property of multiplication or division. 11w + 6 182 17. Fast solutions. Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. Show each step of your work! The same problem occurs when multiplying by a negative number. Equations and inequalities is an essential concept in mathematics. Chapter 1: Solving Equations and Inequalities 4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Quiz 2: 5 questions Practice what you've learned, and level up on the above skills. Solving Linear Equations Worksheet Pdf - Fabad ]br@ .$K@ 8+t By breaking down and clarifying the steps in a math equation, students can more easily understand and solve the problem. Linear inequalities math worksheet for 7th grade children - PDF printable in 7th Grade, Inequalities/by math4childrenplus Linear inequalities worksheet for 7th grade children. \\ x = \frac { 3 } { 9 } = \frac { 1 } { 3 } \end{aligned}\). Simplify 2 6(4 7)2 without using a calculator. Choose AT LEAST one type. PDF Solving Equations and Inequalities Review - gvsd.org \\ \frac { 5 } { 3 } x & = - 10 \\ \color{Cerulean}{\frac { 3 } { 5 }} \color{Black}{ \cdot} \frac { 5 } { 3 } x & = \color{Cerulean}{\frac { 3 } { \cancel{5} }} \color{Black}{\cdot} ( \overset{-2}{\cancel{-10}} )\quad \color{Cerulean}{Multiply \:both \:sides\: by\: \frac{3}{5}.} Each free worksheet can be customized and comes with an answer key. There is no upper end to the solution to this inequality. -A.2B write given point and slope or two points %PDF-1.6 % To get a different worksheet using the same options: Worksheets for evaluating expressions with variables, Worksheets for writing expressions with variables from verbal expressions, Font: Identify the slope constant in the inequality (the 'm' value). Solve and graph the solution set: \(5x+7<22\). PDF format: come back to this page and push the button again. Helvetica 1 0 obj <> endobj 1280 0 obj <>stream \\ - 5 a + 2 = 1 & \quad\color{Cerulean} { Subtract\: 2\: on\: both\: sides.} This product covers all of the Objective 5 TEKS. Worksheets for linear equations - Homeschool Math If given a linear equation of the form \(ax + b = c\), then we can solve it in two steps. Decide mathematic equation To solve a math equation, you need to figure out what the equation is asking for and then use the appropriate operations to solve it. \\ { - 2 \color{OliveGreen}{<}\color{Black}{ 1} \quad \color{Cerulean}{} \color{Cerulean}{ True } } \end{array}\). After translating the sentence into a mathematical statement we then solve. Questions at the stations include solving linear equations by graphing, elimination, and substitution, determining which method is best for solving a given system, finding errors when solving a system, and graphing systems of linear inequalities. Videos, worksheets, 5-a-day and much more 4 0 obj To do this, first use the appropriate equality property of addition or subtraction to isolate the variable term on one side of the equal sign. 50 < 8 - 6x 11. stream Step 1: Simplify both sides of the equation using the order of operations and combine all like terms on the same side of the equal sign. Determine mathematic equation. To do this, use the addition or subtraction property of equality to place like terms on the same side so that they can be combined. 2. Sometimes the generated worksheet is not exactly what you want. 1 0 obj Solving Equations and Inequalities Review Solve each equation or inequality. If you divide or multiply an inequality by a negative number, reverse the inequality to obtain an equivalent inequality. In all the equations we have solved so far, all the variable terms were on . Inequalities worksheets with answer key algebra 1 worksheet printable solving and graphing pdf for 6th grade linear answers in one variable equations single double go teach maths handcrafted resources teachers systems of edboost Inequalities Worksheets With Answer Key Inequalities Algebra 1 Worksheet Printable Inequalities Worksheets With Answer Key Solving And Graphing Inequalities Worksheets . Solve Linear Inequalities Worksheet - Worksheet & Templates Systems of Equations and Inequalities Review Sketch the solution to each system of inequalities. \( \frac { 1 } { 2 } x + \frac { 5 } { 3 }\), \(\begin{aligned} \neq & \color{red}{6 \cdot}\color{Black}{ \left( \frac { 1 } { 2 } x + \frac { 5 } { 3 } \right)} \\ = & 3 x + 10 \quad \color{red}{} \end{aligned}\). Writing and solving linear functions equations and inequalities kuta - In Writing task 1 academic you need to write a report about one of the following: It. An equation is a statement that asserts the equality of two expressions and a linear inequality is an inequality which involves a linear function. \\ x & \leq - 15 \end{aligned}\). Materials needed for each student: scissors, ruler, 2 to 3 markers, and a piece of cardstock or construction paper. AI. Lesson plans are editable. 2011-10-03T14:46:12-04:00 \(\begin{array} { l } { 10 > - 5 } \\ { \frac { 10 } { \color{Cerulean}{- 5} } \color{Black}{>} \frac { - 5 } { \color{Cerulean}{- 5} } } \quad \color{Cerulean}{Divide\: both\: sides\: by\: -5.} Some filters moved to Formats filters, which is at the top of the page. Linear Equations and Inequalities Worksheet - 1, Linear Equations and Inequalities Worksheet - 2, Linear Equations and Inequalities Worksheet - 3, Linear Equations and Inequalities Worksheet - 4. Thelearningodyssey worksheets student solving linear equations Solving Equations and Inequalities Review. We'll also see what it takes for an equation to have no solution, or infinite solutions. WORKSHEETS. In mathematics, an inequality is simply a statement that the quantity on one side of the signs of greater , smaller or equal is not equal to the quantity on the other side of the sign.The answer key in these worksheets is . \\[20pt] 135Equations that are true for particular values.