Question

Find the value of the variable.

$4c+23=9c-7$

Short answer

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

Step-by-step solution

Step 1. Subtract 4c.

First subtract 4c from both sides of the equation $4c+23=9c-7$.

$4c+23-\left(4c\right)=9c-7-\left(4c\right)$

Step 2. Combine the like terms.

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

$\begin{array}{l}4c-4c+23=9c-4c-7\\ 23=5c-7\end{array}$

Step 3. Add 7.

To further simplify, add 7 to both sides of the equation $23=5c-7$.

$\begin{array}{l}23+7=5c-7+7\\ 30=5c\end{array}$

Step 4. Divide by 5.

Divide both sides of the equation $30=5c$by 5 and cancel the common factors of 5 on both sides.

$\begin{array}{l}\frac{30}{5}=\frac{5c}{5}\\ \frac{5\times 6}{5}=c\\ 6=c\end{array}$

Step 5. Verify the value.

In order to verify the value of c, substitute 6 for c into the equation $4c+23=9c-7$and simplify.

$\begin{array}{l}4\times 6+23=9\times 6-7\\ 24+23=54-7\\ 47=47\text{True}\end{array}$

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