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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

1. Solving Equations Using Addition or Subtraction

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Exercise 26 Page 131

Use the Addition Property of Equality to eliminate the subtraction.

r=- 19/20

Practice makes perfect

To solve the equation, we have to isolate r on one side. Using the Addition Property of Equality, we will add 45 to both sides of the equation. This will eliminate the subtraction and isolate r.

- 2 14 = r - 4/5

LHS+4/5=RHS+4/5

- 2 14 + 4/5 = r - 4/5 + 4/5

Add terms

- 2 14 + 4/5 = r

▼

Simplify left-hand side

Write as a difference

- 2 - 1/4 + 4/5 = r

a/b=a * 5/b * 5

- 2 - 5/20 + 4/5 = r

a/b=a * 4/b * 4

- 2 - 5/20 + 16/20 = r

Add terms

- 2 + 11/20 = r

Write as a difference

-1 -1 + 11/20 = r

Rewrite 1 as 20/20

- 1 - 20/20 + 11/20 = r

Add fractions

- 1 - 9/20 = r

Subtract term

- 1 920 = r

Rearrange equation

r = - 1 920

To check that this solution is correct, let's substitute r = - 1 920 into the original equation and simplify.

- 2 14 = r - 4/5

r= - 1 920

- 2 14? = - 1 920 - 4/5

Write as a difference

- 2 14? = - 1 - 9/20 - 4/5

a/b=a * 4/b * 4

- 2 14? = - 1 - 9/20 - 16/20

Subtract fractions

- 2 14? = - 1 - 25/20

a/b=.a /5./.b /5.

- 2 14? = - 1 - 5/4

Write as a difference

- 2 14? = - 1 - 4/4 - 1/4

Calculate quotient

- 2 14? = - 1 - 1 - 1/4

Subtract term

- 2 14 = - 2 14 ✓

Since the left-hand side and right-hand side are equal, r = - 1 920 is the correct solution.

Subchapter links

Try It p.128-129

Self-Assessment for Concept & Skills p.129

Self-Assessment for Problem Solving p.130

Review & Refresh p.131

Concept, Skills, & Problem Solving p.131-132