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

Chapter Review

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Exercise 7 Page 173

Use the Addition Property of Equality to eliminate the subtraction.

t=4.9

Practice makes perfect

To solve the equation, we have to isolate t on one side. Using the Addition Property of Equality, we will add 3.7 to both sides of the equation. This will eliminate the subtraction. Let's do it!

t-3.7=1.2

AddEqn

LHS+3.7=RHS+3.7

t-3.7+3.7=1.2+3.7

AddTerms

Add terms

t=4.9

To check that this solution is correct, let's substitute t=4.9 into the original equation and simplify.

t-3.7=1.2

Substitute

t= 4.9

4.9-3.7? =1.2

SubTerm

Subtract term

1.2=1.2 ✓

Since the left-hand side and right-hand side are equal, t=4.9 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 7 Page 173

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