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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

Chapter Review

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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

LHS-5/8=RHS-5/8

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

Subtract term

w/6=- 1 38-5/8

▼

a bc=a* c+b/c

a bc=a* c+b/c

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

Multiply

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

Add terms

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

MoveNegFracToNum

Put minus sign in numerator

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

Subtract fractions

w/6=- 11-5/8

Subtract term

w/6=- 16/8

Calculate quotient

w/6=- 2

Now, we can continue to solve using the Properties of Equality.

w/6=- 2

LHS * 6=RHS* 6

w/6* 6=- 2* 6

FracMultDenomToNumber

a/6* 6 = a

w=- 2* 6

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

w= - 12

- 12/6+5/8 ? = - 1 38

▼

Simplify

Calculate quotient

- 2+dfrac58? =- 1 38

a = 8* a/8

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

Multiply

- 16/8+dfrac58? =- 1 38

Add fractions

- 16+5/8? =- 1 38

Add terms

- 11/8? =- 1 38

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

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