Question

Algebra Basics Solve the equation. Check your solution. (Lesson 2.5)

$\mathbf{c}\mathbf{+}\mathbf{12}\mathbf{=}\mathbf{23}$

Short answer

The solution for the equation $c+12=23$ is $c=11$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}c+12=23\text{}\left[\text{Writeoriginalequation.}\right]\text{}\\ c+12-12=23-12\text{}\left[\text{Subtract12fromeachside.}\right]\text{}\end{array}$

.  Simplify both sides

Simplify the equation on both sides to solve it.

$\begin{array}{l}c=23-12\\ c=11\end{array}$

Therefore, the solution of the equation is $c=11$.

.  Check the solution 

To check the solution, write the original equation and substitute the value of c.

$c+12=23$

Now, substitute $c=11$and check the result.

$\begin{array}{l}c+12=23\text{}\left[\text{Writeoriginalequation.}\right]\text{}\\ 11+12=23\text{}\left[\text{Substitute}1\text{1forc.}\right]\text{}\\ 23=23\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.