Question

Find the value of the variable.

$12=3r-9$

Short answer

The value of the variable is $\mathit{r}\mathbf{=}\mathbf{7}$.

Step-by-step solution

Step 1. Add 9.

To find the value of variable r in the equation $12=3r-9$, add 9 on both sides of the equation.

$12+\left(9\right)=3r-9+\left(9\right)$

Step 2. Simplify the equation.

To simplify, remove all the brackets and combine the like terms.

$\begin{array}{l}12+9=3r-9+\left(9\right)\\ 21=3r\end{array}$

Step 3. Divide by 3.

To find the value of variable r in the equation $21=3r$, divide both sides of the equation by 3.

$\frac{21}{3}=\frac{3r}{3}$

Step 4. Simplify the equation.

To further simplify, cancel the common factors of 3 on both sides.

$\begin{array}{l}\frac{3\times 7}{3}=\frac{3r}{3}\\ 7=r\end{array}$

Step 5. Verify the value.

In order to verify the value of r, substitute 7 for r into the equation $12=3r-9$.

$\begin{array}{l}12=3\times 7-9\\ 12=21-9\\ 12=12\text{True}\end{array}$

Hence, the value of the variable is $r=7$.