Question

Find the value of the variable.

$12+3b=2+5b$

Short answer

The value of the variable is $\mathit{b}\mathbf{=}\mathbf{5}$.

Step-by-step solution

Step 1. Subtract 3b.

First subtract 3b from both sides of the equation $12+3b=2+5b$.

$12+3b-\left(3b\right)=2+5b-\left(3b\right)$

Step 2. Combine the like terms.

To further simplify open the brackets and combine the like terms.

$\begin{array}{l}12+3b-3b=2+5b-3b\\ 12=2+2b\end{array}$

Step 3. Subtract 2.

To further simplify, subtract 2 from both sides of the equation $12=2+2b$.

$\begin{array}{l}12-2=2+2b-2\\ 10=2b\end{array}$

Step 4. Divide by 2.

Divide both sides of the equation $10=2b$by 2 and cancel the common factors of 2 on both sides.

$\begin{array}{l}\frac{10}{2}=\frac{2b}{2}\\ \frac{5\times 2}{2}=b\\ 5=b\end{array}$

Step 5. Verify the value.

In order to verify the value of b, substitute 5 for b into the equation$12+3b=2+5b$and simplify.

$\begin{array}{c}12+3\times 5=2+5\times 5\\ 12+15=2+25\\ 27=27\text{True}\end{array}$

Hence, the value of the variable is $b=5$.