Question

Find the value of the variable.

$2p+5=13$

Short answer

The value of the variable is $\mathit{p}\mathbf{=}\mathbf{4}$.

Step-by-step solution

Step 1. Subtract 5.

To find the value of variable p in the equation $2p+5=13$, subtract 5 from both sides of the equation.

$2p+5-\left(5\right)=13-\left(5\right)$

Step 2. Simplify the equation.

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

$\begin{array}{l}2p+5-5=13-5\\ 2p=8\end{array}$

Step 3. Divide by 2.

To find the value of the variable p in the equation $2p=8$, divide both sides of the equation by 2.

$\frac{2p}{2}=\frac{8}{2}$

Step 4. Simplify the equation.

To further simplify, cancel the common factors of 2 on both sides.

$\begin{array}{l}\frac{2p}{2}=\frac{2\times 4}{2}\\ p=4\end{array}$

Step 5. Verify the value.

In order to verify the value of p, substitute 4 for p into the equation $2p+5=13$.

$\begin{array}{l}2\times 4+5=13\\ 8+5=13\\ 13=13\text{True}\end{array}$

Hence, the value of the variable is $p=4$.