Q28. - Algebra 1

Question

Use the Distributive Property to rewrite each expression. Then simplify.

$\mathbf{-}\mathbf{3}\mathbf{(}\mathbf{2}\mathit{x}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{6}\mathbf{)}$

Step-by-Step Solution

Answer

The simplified form of $-3\left(2x-6\right)$ is $\mathbf{-}\mathbf{6}\mathit{x}\mathbf{+}\mathbf{18}$.

Step 1. Use the distributive property.

The distributive law of multiplication over addition or subtraction states that, $a\left(b\pm c\right)=ab\pm ac$.

So, the values of $a,b, \mathrm{and} c$ should be as follows:

$\begin{array}{l}a=-3\\ b=2x\\ c=6\end{array}$

Step 2. Rewrite the expression.

Use the distributive property to expand the expression further as shown below:

$\text{-3}\left(2x-6\right)=\left(-3\right)2x-\left(-3\right)6$

Step 3. Evaluate the expression.

To simplify further, multiply the numbers and solve further as shown below:

$\begin{array}{l}-3\left(2x-6\right)\text{=}\left(\text{-3}\right)\text{2x-}\left(\text{-3}\right)6 \left[Multiply\right]\\ =-6x-\left(-18\right)\\ =-6x+18\end{array}$