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

Chapter Review

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Exercise 2 Page 173

Use the Subtraction Property of Equality to eliminate the addition.

q=- 5

Practice makes perfect

To solve the equation, we have to isolate q on one side. Using the Subtraction Property of Equality, we will subtract 6 from both sides of the equation. This will eliminate the addition. Let's do it!

6+q=1

SubEqn

LHS-6=RHS-6

6+q-6=1-6

CommutativePropAdd

Commutative Property of Addition

q+6-6=1-6

SubTerm

Subtract term

q=- 5

To check that this solution is correct, let's substitute q=- 5 into the original equation and simplify.

6+q=1

Substitute

q= - 5

6+( - 5)? =1

AddNeg

a+(- b)=a-b

6-5? =1

SubTerm

Subtract term

1=1 ✓

Since the left-hand side and right-hand side are equal, q=- 5 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 2 Page 173

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