Question

Solve $\left|6m-3\right|=9$

F. $\left\{2\right\}$
H. $\left\{-3,6\right\}$

G. $\left\{-1,2\right\}$

J. $\left\{-3,3\right\}$

Short answer

Option (G) is the correct.

Step-by-step solution

Step 1. Given equation.

$\left|6m-3\right|=9$

Step 2. absolute value.

Absolute value is written as:

$\left|x\right|=\left\{\begin{array}{l}x;\text{if}x\ge 0\\ -x;\text{if}x<0\end{array}\right.$

Step 3. Description of step.

To find the value of m, solve the equation by simplifying the absolute value in $\left|6m-3\right|=9$, as

$$\begin{gathered} \left|6m-3\right|=9 \\ 6m-3=9\text{and}6m-3=-9 \\ \Rightarrow 6m=9+3\text{and}6m=-9+3 \\ \Rightarrow 6m=12\text{and}6m=-6 \\ \Rightarrow m=2\text{and}m=-1 \\ \Rightarrow m=\left\{-1,2\right\} \end{gathered}$$

Thus, option (G) is the correct.