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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

4. Rewriting Equations and Formulas

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Exercise 17 Page 29

Apply inverse operations to isolate y.

y=3x-1.5

Practice makes perfect

To solve the given literal equation for y, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.

4.2x-1.4y=2.1

LHS-4.2x=RHS-4.2x

4.2x-1.4y-4.2x=2.1-4.2x

Subtract term

- 1.4y=2.1-4.2x

Now, we can use the Division Property to simplify the equation even further.

- 1.4y=2.1-4.2x

.LHS /- 1.4.=.RHS /- 1.4.

- 1.4y/- 1.4=2.1-4.2x/- 1.4

Calculate quotient

y=2.1-4.2x/- 1.4

▼

Simplify left-hand side

Write as a difference of fractions

y=2.1/- 1.4-4.2x/- 1.4

MoveNegDenomToFrac

Put minus sign in front of fraction

y=- 2.1/1.4-(-4.2x/1.4)

a-(- b)=a+b

y=-2.1/1.4+4.2x/1.4

Factor out 0.7

y=- 0.7(3)/0.7(2)+0.7(6x)/0.7(2)

CancelCommonFac

Cancel out common factors

y=- 0.7(3)/0.7(2)+0.7(6x)/0.7(2)

Simplify quotient

y=- 3/2+6x/2

MovePartNumRight

a* b/c=a/c* b

y=- 3/2+6/2x

Calculate quotient

y=- 3/2+3x

Write as a decimal

y=- 1.5+3x

CommutativePropAdd

Commutative Property of Addition

y=3x-1.5

Subchapter links

Try It p.26-27

Self-Assessment for Concepts & Skills p.27

Self-Assessment for Problem Solving p.28

Review & Refresh p.29

Concepts, Skills, & Problem Solving p.29-30