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Big Ideas Math: Modeling Real Life, Grade 7 View details

Chapter Review

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Exercise 13 Page 173

Use the Multiplication Property of Equality to eliminate the division.

y=- 49

Practice makes perfect

To solve the equation, we have to isolate y on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 7. This will eliminate the denominator of the fraction and isolate y.

- 7=y/7

RearrangeEqn

Rearrange equation

y/7=- 7

MultEqn

LHS * 7=RHS* 7

y/7*7=- 7*7

FracMultDenomToNumber

a/7* 7 = a

y=- 7*7

Multiply

y=- 49

To check that this solution is correct, let's substitute y=- 49 into the original equation and simplify.

- 7=y/7

Substitute

y= - 49

- 7? =- 49/7

CalcQuot

Calculate quotient

- 7=- 7 ✓

Since the left-hand side and right-hand side are equal, y=- 49 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.

Subchapter links

1 Solving Equations Using Addition or Subtraction p.173

2 Solving Equations Using Multiplication or Division p.173

3 Solving Two-Step Equations p.174

4 Writing and Graphing Inequalities p.174

5 Solving Inequalities Using Addition or Subtraction p.174-175

6 Solving Inequalities Using Multiplication or Division p.175

7 Solving Two-Step Inequalities p.175

Exercise 13 Page 173

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