Question

graph the solution set of the equation.
$|3x - 2| = 7$

Explanation:

Step1: Split absolute value equation

For $|3x - 2| = 7$, we get two cases:
$3x - 2 = 7$ or $3x - 2 = -7$

Step2: Solve first linear equation

Isolate $x$:
$3x = 7 + 2$
$3x = 9$
$x = \frac{9}{3} = 3$

Step3: Solve second linear equation

Isolate $x$:
$3x = -7 + 2$
$3x = -5$
$x = \frac{-5}{3} \approx -1.67$

Step4: Identify graph type

The solution set is two distinct points, so we use closed dots on $x=3$ and $x=-\frac{5}{3}$ on the number line, matching the first icon (single closed dot style, applied to both points).

Answer:

The solution set is $x=3$ and $x=-\frac{5}{3}$. On the number line, plot closed dots at $3$ and $-\frac{5}{3}$ (between -2 and -1), corresponding to the first provided graph icon (single closed dot) placed at these two positions.