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Equations and inequalities

Mathematics, Grade 8

Equations and inequalities

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Study Guide Equations and inequalities Mathematics, Grade 8

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EQUATIONS AND INEQUALITIES What Are Equations and Inequalities? An equation is mathematical statement that shows that two expressions are equal to each other. • The expressions used in an equation can contain variables or numbers. • An equation can be in verbal form or algebraic form. • Equations are solved by using inverse operations. Inverse operations are used to isolate a variable. Inverse operations undo an operation; addition is the inverse operation of subtraction and multiplication is the inverse operation of division and vice versa. • Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; a nd less than or equal to, ≤. Inequalities are also solved by using inverse operations. How to use Equations and Inequalities • The statement, x + 4 = 7, is an example of an equation. Another example of an equation is twenty-two times a number is one hundred and ten. The algebraic representation of this is 22x = 110. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• Equations are solved using the inverse operations. To solve the equation n - 52 = 38, look to see what operation is being performed in the problem, subtraction. The problem can be solved using the inverse operation of addition as the example shows: n - 52 = 38 + 52 +52 n = 90 Since 52 was subtracted in the initial problem, it will be added with inverse operations. The rule when dealing with equations is whatever is done to one side of the equation must be done to the other side. So 52 is added to 38 on the other side of the equal sign. When both sides are added, the numbers on the left side of the equation will cancel out, leaving only the n. On the right side of the equation, 38 and 52 are added, giving the answer of 90. Therefore n = 90. • Inequalities are solved the same way as algebraic equations by using inverse operations. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Ex. x + 3 ≥ 7 -2x < 28 - 3 -3 -2 -2 x ≥ 4 x > -14 ← (notice sign is reversed) © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 1. Translate into an algebraic equation: Six times a number diminished two is twenty-eight. A number increased by seven squared is fifty-four. 2. Solve if n = 3: 7 - n² 4n + 8 9n² ÷ 3 3. Solve the following equations: x + 14 = 22 5x = 105 x/2 = 98 4. Solve the following inequalities: x + 27 ≤ -12 x - 12 > -36 8x < -128 x/-2 ≥ 18 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Equations and inequalities

Mathematics, Grade 8

Equations and inequalities

Study Guide

Equations and inequalities

Flash Cards

Equations and inequalities

Quiz

Equations and inequalities

Worksheets

Equations and inequalities

Games

Study Guide Equations and inequalities Mathematics, Grade 8

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