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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

3. Solving Equations with Variables on Both Sides

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Exercise 8 Page 19

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

Infinitely many solutions

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.

1/3(2b+9)=2/3(b+9/2)

Distribute 13

2b* 1/3+9* 1/3=2/3(b+9/2)

MoveLeftFacToNumOne

a* 1/b= a/b

2/3b+9/3=2/3(b+9/2)

Calculate quotient

2/3b+3=2/3(b+9/2)

Distribute 23

2/3b+3=2/3b+2/3* 9/2

Multiply fractions

2/3b+3=2/3b+18/6

Calculate quotient

2/3b+3=2/3b+3

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

2/3b+3=2/3b+3

LHS- 23b=RHS- 23b

2/3b+3-2/3b=2/3b+3-2/3b

Subtract term

3=3

Simplifying the equation resulted in an identity. Therefore, the equation has infinitely many solutions.

Subchapter links

Try It p.18-20

Self-Assessment for Concepts & Skills p.20

Self-Assessment for Problem Solving p.21

Review & Refresh p.22

Concepts, Skills, & Problem Solving p.22-24