Answer
B
Work Step by Step
An equation with an absolute value in it is equivalent to two equations together, in this case, $|3x+7|=5x$ is equivalent to $3x+7=5x$ and $3x+7=-5x$. Solve for x in each equation:
I) $3x+7=5x$
Subtract 3x from each side:
$7=5x-3x$
$7=(5-3)x$
$7=2x$
Divide both sides by 2:
$x=\frac72$
II) $3x+7=-5x$
Subtract 3x from each side:
$7=-5x-3x$
$7=(-5-3)x$
$7=-8x$
Divide both sides by -8:
$x=-\frac78$
The two solutions for this equation are then $-\frac78$ and $\frac72$, so the correct option is B.
