Answer
$B$
Work Step by Step
Use the rule $|x|=a \implies x=a \text{ or } x=-a$ to obtain:
$3x - 5 = 2\quad$ or $\quad3x - 5 = -2$
Solve each equation.
For the first equation we have:
$3x - 5 = 2$
$3x = 2+5\\
3x=7$
Divide both sides of the equation by $3$ to solve for $x$:
$x = \frac{7}{3}$
For the second equation:
$3x - 5 = -2\\
3x=-2+5$
$3x = 3$
Divide both sides of the equation by $3$ to solve for $x$:
$x = 1$
Thus, the solutions are $x = \frac{7}{3}$ and $x = 1$. This corresponds to option $B$.
