Warm Up Solutions

Use the Formula Sheet to name the property used to solve the equation.

$\begin{array}{rcl} \frac{4}{3} (2 x - 5) & = & - 12 \end{array}$

Implement

$\begin{array}{rcl} (\frac{3}{4}) \frac{4}{3} (2 x - 5) & = & - 12 (\frac{3}{4}) \end{array}$

Explain

Multiplication of Property of Equality

$\begin{array}{rcl} 2 x - 5 & = & - 9 \\ + 5 + 5 \end{array}$

Addition Property of Equality

$\begin{array}{rcl} (\frac{1}{2}) 2 x & = & - 4 (\frac{1}{2}) \end{array}$

Multiplication Property of Equality

$\begin{array}{rcl} x & = & - 2 \end{array}$

Simplify

Note

You should recall from Algebra 1 that each step to solving has a justification. Being able to Explain your reasoning is a critical part of any level in mathematics.

Simplify without using a calculator.

$9^{\frac{3}{2}}$

${(9^{\frac{1}{2}})}^{3} {(3)}^{3} 27$

${(- 32)}^{\frac{2}{5}}$

${(- 32^{\frac{1}{5}})}^{2} {(- 2)}^{2} 4$