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Big Ideas Math: Modeling Real Life, Grade 7

BI

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

Chapter Review

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Exercise 1 Page 173

Use the Addition Property of Equality to eliminate the subtraction.

p=- 1

Practice makes perfect

To solve the equation, we have to isolate p on one side. Using the Addition Property of Equality, we will add 3 to both sides of the equation. This will eliminate the subtraction. Let's do it!

p-3=-4

LHS+3=RHS+3

p-3+3=- 4+3

Add terms

p=- 1

To check that this solution is correct, let's substitute p=- 1 into the original equation and simplify.

p-3=-4

p= - 1

- 1-3? =-4

Subtract term

- 4=- 4 ✓

Since the left-hand side and right-hand side are equal, p=- 1 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