Question

Find the value of the variable.

$3p-5=13$

Short answer

The value of the variable is $\mathit{p}\mathbf{=}\mathbf{6}$.

Step-by-step solution

Step 1. Add 5.

To find the value of the variable p in the equation $3p-5=13$, add 5 on both sides of the equation.

$3p-5+\left(5\right)=13+\left(5\right)$

Step 2. Simplify the equation.

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

$\begin{array}{l}3p-5+5=13+5\\ 3p=18\end{array}$

Step 3. Divide by 3.

To find the value of variable p in the equation $3p=18$, divide both sides of the equation by 3.

$\frac{3p}{3}=\frac{18}{3}$

Step 4. Simplify the equation.

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

$\begin{array}{l}\frac{3p}{3}=\frac{3\times 6}{3}\\ p=6\end{array}$

Step 5. Verify the value.

In order to verify the value of p, substitute 6 for p into the equation $3p-5=13$.

$\begin{array}{l}3\times 6-5=13\\ 18-5=13\\ 13=13\text{True}\end{array}$

Hence, the value of the variable is $p=6$.