Question

Solve the equation. Check the solutions.

$|15+m|=-2m+3$

Short answer

The values are $m=-4$.

Step-by-step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Step 2- Simplify the expression.

Consider the expression $|15+m|=-2m+3$.

Step 3- Step description.

Apply the absolute rule as follows:

Case 1. When $15+m=-\left(-2m+3\right)$.

$\begin{array}{l}15+m=-(-2m+3)\\ 15+m=2m-3\\ 15+m-2m+3=0\\ -m+18=0\\ -m=-18\\ m=18\end{array}$

Case 2. When $15+m=\left(-2m+3\right)$

$\begin{array}{l}15+m=(-2m+3)\\ 15+m+2m-3=0\\ 3m+12=0\\ 3m=-12\\ m=-4\end{array}$

Therefore, the value is $m=-4,18$.

Step 4-Verify the solutions.

Substitute $m=-4,18$in the equation $|15+m|=-2m+3$and simplify as follows:

$\begin{array}{l}|15+m|=-2m+3\\ |15-4|=-2(-4)+3\\ \left|11\right|=8+3\\ 11=11\end{array}$

localid="1647480714811" $\begin{array}{l}|15+m|=-2m+3\\ |15+18|=-2\left(18\right)+3\\ \left|33\right|=-36+3\\ 33\ne -33\end{array}$

Since the left-hand side and right-hand side is equal in the first case but not in the second case thus the values are $m=-4$.