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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

Chapter Review

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Exercise 16 Page 418

Isolate the variable term on one side of the equation, then take the cube root of both sides.

x=-8

Practice makes perfect

We want to solve the given equation. -55=1/4x^3+73First, we will use the Properties of Equality to isolate the variable term on one side of the equation.

-55=1/4x^3+73

LHS-73=RHS-73

-128=1/4x^3

LHS * 4=RHS* 4

-512=1/4x^3*4

MoveRightFacToNumOne

1/b* a = a/b

-512=4/4x^3

a/a=1

-512=x^3

Rearrange equation

x^3=-512

Next, we take the cube root on both sides of the equation. We do this because x is raised to the third power. Let's do it!

x^3=-512

sqrt(LHS)=sqrt(RHS)

sqrt(x^3)=sqrt(-512)

SplitIntoFactors

Split into factors

sqrt(x^3)=sqrt((-8)*(-8)*(-8))

ProdToPowThreeFac

a* a* a=a^3

sqrt(x^3)=sqrt((-8)^3)

RootPowToNumber

sqrt(a^3)=a

x=-8

The value of x is -8.

Subchapter links

1 Finding Square Roots p.417

2 The Pythagorean Theorem p.417

3 Finding Cube Roots p.418

4 Rational Numbers p.418

5 Irrational Numbers p.419

6 The Converse of the Pythagorean Theorem p.419