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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 27 Page 131

Use the Subtraction Property of Equality to eliminate the addition.

w = - 1 1324

Practice makes perfect

To solve the equation, we have to isolate w on one side. Using the Subtraction Property of Equality, we will subtract 3 38 from both sides of the equation. This will eliminate the addition and isolate w.

w + 3 38 = 1 56
SubEqn

LHS-3 38=RHS-3 38

w + 3 38 - 3 38 = 1 56 - 3 38
SubTerm

Subtract term

w = 1 56 - 3 38
â–¼
Simplify right-hand side
WriteSum

Write as a sum

w = 1 + 5/6 - 3 38
WriteDiff

Write as a difference

w = 1 + 5/6 - 3 - 3/8
CommutativePropAdd

Commutative Property of Addition

w = 1 - 3 + 5/6 - 38
ExpandFrac

a/b=a * 4/b * 4

w = 1 - 3 + 20/24 - 38
ExpandFrac

a/b=a * 3/b * 3

w = 1 - 3 + 20/24 - 924
SubTerms

Subtract terms

w = - 2 + 11/24
WriteDiff

Write as a difference

w = - 1 - 1 + 11/24
OneToFrac

Rewrite 1 as 24/24

w = - 1 - 24/24 + 11/24
AddTerms

Add terms

w = - 1 - 13/24
SubTerm

Subtract term

w = - 1 1324

To check that this solution is correct, let's substitute w = - 1 1324 into the original equation and simplify.

w + 3 38 = 1 56
Substitute

w= - 1 1324

- 1 1324 + 3 38 ? = 1 56
WriteSum

Write as a sum

- 2 + 11/24 + 3 + 3/8? = 1 56
ExpandFrac

a/b=a * 3/b * 3

- 2 + 11/24 + 3 + 9/24? = 1 56
CommutativePropAdd

Commutative Property of Addition

- 2 + 3 + 11/24 + 9/24? = 1 56
AddTerms

Add terms

1 + 20/24 ? = 1 56
ReduceFrac

a/b=.a /4./.b /4.

1 + 5/6 ? = 1 56
AddTerms

Add terms

1 56 = 1 56 ✓

Since the left-hand side and right-hand side are equal, w = - 1 1324 is the correct solution.

Subchapter links expand_more
arrow_right Try It p.128-129
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Try It 2 (Page 128)
Try It 3 (Page 128)
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arrow_right Self-Assessment for Concept & Skills p.129
Self-Assessment for Concept & Skills 5 (Page 129)
Self-Assessment for Concept & Skills 6 (Page 129)
Self-Assessment for Concept & Skills 7 (Page 129)
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arrow_right Self-Assessment for Problem Solving p.130
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arrow_right Review & Refresh p.131
Review & Refresh 1 (Page 131)
Review & Refresh 2 (Page 131)
Review & Refresh 3 (Page 131)
Review & Refresh 4 (Page 131)
Review & Refresh 5 (Page 131)
Review & Refresh 6 (Page 131)
Review & Refresh 7 (Page 131)
Review & Refresh 8 (Page 131)
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arrow_right Concept, Skills, & Problem Solving p.131-132
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Concept, Skills, & Problem Solving 11 (Page 131)
Concept, Skills, & Problem Solving 12 (Page 131)
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Concept, Skills, & Problem Solving 45 (Page 132)
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