Question

which expression is equivalent to 5(-3x - 9) - 9x? -3(-9x + 5) - 9x -9(-3x + 5) - 9x 5(-6x + 3x - 9) - 9x -3(5x - 9) - 9x

Explanation:

Step1: Expand the original expression

\[

$$\begin{align*} 5(-3x - 9)-9x&=5\times(-3x)+5\times(-9)-9x\\ &=-15x-45 - 9x\\ &=(-15x-9x)-45\\ &=-24x - 45 \end{align*}$$

\]

Step2: Expand option A

\[

$$\begin{align*} -3(-9x + 5)-9x&=(-3)\times(-9x)+(-3)\times5-9x\\ &=27x-15 - 9x\\ &=(27x-9x)-15\\ &=18x-15 \end{align*}$$

\]

Step3: Expand option B

\[

$$\begin{align*} -9(-3x + 5)-9x&=(-9)\times(-3x)+(-9)\times5-9x\\ &=27x-45 - 9x\\ &=(27x-9x)-45\\ &=18x-45 \end{align*}$$

\]

Step4: Expand option C

\[

$$\begin{align*} 5(-6x + 3x-9)-9x&=5(-3x-9)-9x\\ &=5\times(-3x)+5\times(-9)-9x\\ &=-15x-45 - 9x\\ &=-24x-45 \end{align*}$$

\]

Step5: Expand option D

\[

$$\begin{align*} -3(5x - 9)-9x&=(-3)\times5x+(-3)\times(-9)-9x\\ &=-15x + 27-9x\\ &=(-15x-9x)+27\\ &=-24x+27 \end{align*}$$

\]

Answer:

C. \(5(-6x + 3x - 9)-9x\)