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Big Ideas Math: Modeling Real Life, Grade 7
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Exercise 26 Page 174

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

w=- 12

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Subtraction Property of Equality to simplify the left- and right-hand sides of the equation.

w/6+5/8=- 1 38
SubEqn

LHS-5/8=RHS-5/8

w/6+5/8-5/8=- 1 38-5/8
SubTerm

Subtract term

w/6=- 1 38-5/8
â–¼
a bc=a* c+b/c
MixedToFrac

a bc=a* c+b/c

w/6=- 1* 8+3/8-5/8
Multiply

Multiply

w/6=- 8+3/8-5/8
AddTerms

Add terms

w/6=- 11/8-5/8
MoveNegFracToNum

Put minus sign in numerator

w/6=- 11/8-5/8
SubFrac

Subtract fractions

w/6=- 11-5/8
SubTerm

Subtract term

w/6=- 16/8
CalcQuot

Calculate quotient

w/6=- 2
Now, we can continue to solve using the Properties of Equality.

w/6=- 2
MultEqn

LHS * 6=RHS* 6

w/6* 6=- 2* 6
FracMultDenomToNumber

a/6* 6 = a

w=- 2* 6
Multiply

Multiply

w=- 12

The solution to the equation is w=- 12. We can check our solution by substituting it into the original equation.

w/6+5/8=- 1 38
Substitute

w= - 12

- 12/6+5/8 ? = - 1 38
â–¼
Simplify
CalcQuot

Calculate quotient

- 2+dfrac58? =- 1 38
NumberToFrac

a = 8* a/8

- 2* 8/8+dfrac58? =- 1 38
Multiply

Multiply

- 16/8+dfrac58? =- 1 38
AddFrac

Add fractions

- 16+5/8? =- 1 38
AddTerms

Add terms

- 11/8? =- 1 38
FracToMixed

Write fraction as a mixed number

- 1 38=- 1 38

Since the left-hand side is equal to the right-hand side, our solution is correct.

Extra

 Learn More!
Are you having trouble learning how to solve equations? Would you like to see why the Properties of Equality work? Do real-world examples help you understand more about the why and how of math topics? If you answered Yes to any of these questions, check out the Mathleaks courses related to this topic!

Subchapter links expand_more
arrow_right 1 Solving Equations Using Addition or Subtraction p.173
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Solving Equations Using Addition or Subtraction 2 (Page 173)
Solving Equations Using Addition or Subtraction 3 (Page 173)
Solving Equations Using Addition or Subtraction 4 (Page 173)
Solving Equations Using Addition or Subtraction 5 (Page 173)
Solving Equations Using Addition or Subtraction 6 (Page 173)
Solving Equations Using Addition or Subtraction 7 (Page 173)
Solving Equations Using Addition or Subtraction 8 (Page 173)
Solving Equations Using Addition or Subtraction 9 (Page 173)
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arrow_right 2 Solving Equations Using Multiplication or Division p.173
Solving Equations Using Multiplication or Division 12 (Page 173)
Solving Equations Using Multiplication or Division 13 (Page 173)
Solving Equations Using Multiplication or Division 14 (Page 173)
Solving Equations Using Multiplication or Division 15 (Page 173)
Solving Equations Using Multiplication or Division 16 (Page 173)
Solving Equations Using Multiplication or Division 17 (Page 173)
Solving Equations Using Multiplication or Division 18 (Page 173)
Solving Equations Using Multiplication or Division 19 (Page 173)
Solving Equations Using Multiplication or Division 20 (Page 173)
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arrow_right 3 Solving Two-Step Equations p.174
Solving Two-Step Equations 23 (Page 174)
Solving Two-Step Equations 24 (Page 174)
Solving Two-Step Equations 25 (Page 174)
Solving Two-Step Equations 26 (Page 174)
Solving Two-Step Equations 27 (Page 174)
Solving Two-Step Equations 28 (Page 174)
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arrow_right 4 Writing and Graphing Inequalities p.174
Writing and Graphing Inequalities 30 (Page 174)
Writing and Graphing Inequalities 31 (Page 174)
Writing and Graphing Inequalities 32 (Page 174)
Writing and Graphing Inequalities 33 (Page 174)
Writing and Graphing Inequalities 34 (Page 174)
Writing and Graphing Inequalities 35 (Page 174)
Writing and Graphing Inequalities 36 (Page 174)
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arrow_right 5 Solving Inequalities Using Addition or Subtraction p.174-175
Solving Inequalities Using Addition or Subtraction 38 (Page 174)
Solving Inequalities Using Addition or Subtraction 39 (Page 174)
Solving Inequalities Using Addition or Subtraction 40 (Page 174)
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arrow_right 6 Solving Inequalities Using Multiplication or Division p.175
Solving Inequalities Using Multiplication or Division 43 (Page 175)
Solving Inequalities Using Multiplication or Division 44 (Page 175)
Solving Inequalities Using Multiplication or Division 45 (Page 175)
Solving Inequalities Using Multiplication or Division 46 (Page 175)
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arrow_right 7 Solving Two-Step Inequalities p.175
Solving Two-Step Inequalities 48 (Page 175)
Solving Two-Step Inequalities 49 (Page 175)
Solving Two-Step Inequalities 50 (Page 175)
Solving Two-Step Inequalities 51 (Page 175)
Solving Two-Step Inequalities 52 (Page 175)
Solving Two-Step Inequalities 53 (Page 175)
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