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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 16 Page 265

Express both sides of the inequality as powers with the same base.

x>-2/3

Practice makes perfect

To solve the given exponential inequality, we will start by expressing both sides as powers with the same base.

9^(x-2) > ( 1/81 ) ^(x+2)

WritePow

Write as a power

9^(x-2) > ( 1/9^2 ) ^(x+2)

FracToNegExponent

1/a^m=a^(- m)

9^(x-2) >( 9^(- 2)) ^(x+2)

PowPow

(a^m)^n=a^(m* n)

9^(x-2) > 9^(- 2(x+2))

Distr

Distribute -2

9^(x-2) > 9^(- 2x-4)

Now that both sides of the inequality are expressed as powers of 9, we will use the Property of Inequality for Exponential Functions. This property tells us that if the bases are the same, we only need to compare the exponents. 9^(x-2) > 9^(- 2x-4) ⇔ x-2 > - 2x-4 Let's solve the exponent inequality for x.

x-2 > - 2x-4

▼

Solve for x

AddIneq

LHS+2x>RHS+2x

3x-2 > - 4

AddIneq

LHS+2>RHS+2

3x > -2

DivIneq

.LHS /3.>.RHS /3.

x > - 2/3