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Big Ideas Math: Modeling Real Life, Grade 7

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

Chapter Review

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Exercise 3 Page 173

Use the Subtraction Property of Equality to eliminate the addition.

j=20

Practice makes perfect

To solve the equation, we have to isolate j on one side. Using the Subtraction Property of Equality, we will subtract - 2 from both sides of the equation. This will eliminate the addition. Let's do it!

- 2+j=- 22

LHS-(- 2)=RHS-(- 2)

- 2+j-(- 2)=- 22-(- 2)

a-(- b)=a+b

- 2+j+2=- 22+2

CommutativePropAdd

Commutative Property of Addition

- 2+2+j=- 22+2

Add terms

j=- 20

To check that this solution is correct, let's substitute j=- 20 into the original equation and simplify.

- 2+j=- 22

j= - 20

- 2+( - 20)? =- 22

a+(- b)=a-b

- 2-20? =- 22

Subtract term

- 22=- 22 ✓

Since the left-hand side and right-hand side are equal, j=- 20 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