Answer
The solution is $x=$ $\dfrac{11}{8}$.
Work Step by Step
You are given the equation $2|3x-7|=10x-8$.
Divide both sides by $2$:
$2|3x-7|=10x-8$
$|3x-7|=$ $\dfrac{10x-8}{2}$
$|3x-7|=5x-4$
Separate into two equations:
$3x-7=5x-4$ $or$ $3x-7=-(5x-4)$
Solve:
$3x-7=5x-4$
$-7=2x-4$
$-3=2x$
$x=-$ $\dfrac{3}{2}$
Second equation:
$3x-7=-(5x-4)$
$3x-7=-5x-4$
$8x-7=4$
$8x=11$
$x=$$\dfrac{11}{8}$
The solution is $x=$ $\dfrac{11}{8}$ and $x=-$ $\dfrac{3}{2}$ is an extraneous solution.
