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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

4. Rewriting Equations and Formulas

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Exercise 2 Page 29

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

z=6

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 Distributive Property to simplify the left- and right-hand sides of the equation.

4(z-3)=2z

Distribute 4

4z-12=2z

LHS-2z=RHS-2z

4z-12-2z=2z-2z

Subtract term

2z- 12=0

LHS+12=RHS+12

2z- 12+12=0+12

Add terms

2z=12

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

2z=12

.LHS /2.=.RHS /2.

2z/2=12/2

Calculate quotient

z=6

The solution to the equation is z=6. We can check our solution by substituting it into the original equation.

4(z-3)=2z

z= 6

4( 6-3) ? = 2( 6)

▼

Simplify

Subtract term

4(3) ? = 2(6)

Multiply

12=12

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

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