91Ó°ÊÓ

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.

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

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 $m=-4,18$.

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" $\begin{array}{l}|15+m|=−2m+3\\ |15+18|=−2\left(18\right)+3\\ \left|33\right|=−36+3\\ 33≠−33\end{array}$

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 $m=-4$.