Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 42

Evaluate the equation $|2x - 5| = |x + 4|$. Then give the solution in set notation.
By using the property of Absolute value, we have

$
\begin{equation}
\begin{aligned}
2x -5 &= x + 4 && \text{and} & 2x - 5 &= -(x + 4)
&& \text{Apply Distributive Property}\\
\\
2x -5 &= x + 4 && \text{and} & 2x -5 &= - x - 4
&& \text{Evaluate}\\
\\
2x -x &= 4 + 5 && \text{and} & 2x + x &= -4 + 5
&& \text{Group like terms}\\
\\
x &= 9 && \text{and} & 3x &= 1
&& \text{Solve for } x\\
\\
&&&& x &= \frac{1}{3}
\end{aligned}
\end{equation}
$

Thus, the solution set is $\displaystyle \left\{ \frac{1}{3}, 9 \right\}$