Answer
$\left\{\dfrac{11}{10},\dfrac{7}{2}\right\}$
Work Step by Step
The given equation, $
|6x-9|=|-4x+2|
$ is equivalent to
\begin{align*}
6x-9&=-4x+2
\\\text{ OR }\\
6x-9&=-(-4x+2)
.\end{align*}
Solving these equations separately results to
\begin{array}{l|r}
6x-9=-4x+2 & 6x-9=-(-4x+2)
\\
6x+4x=2+9 & 6x-9=4x-2
\\
10x=11 & 6x-4x=-2+9
\\\\
x=\dfrac{11}{10} & 2x=7
\\\\
& x=\dfrac{7}{2}
.\end{array}
Hence, the solution set of the equation $
|6x-9|=|-4x+2|
$ is $\left\{\dfrac{11}{10},\dfrac{7}{2}\right\}$.
