Set up two equations: one where $2x - 7$ equals a positive number, and one where $2x - 7$ equals the corresponding negative number. Then solve each equation for $x$.

After you find the possible values of $x$, compare them to the answer choices. You can also plug each choice into $|2x - 7|$ to see which one makes the equation true.

In Desmos, type y = |2x - 7| on one line and y = 3 on another line so you can see where the graphs intersect.

Click on the points where the V-shaped graph of $y = |2x - 7|$ meets the horizontal line $y = 3$. Note the $x$-coordinates of these intersection points, and then see which of the answer choices matches one of those $x$-values.

The equation is

By definition, $|A| = 3$ means $A = 3$ or $A = -3$. Here, $A$ is $2x - 7$, so we write two equations:

• $2x - 7 = 3$
• $2x - 7 = -3$.

Solve each equation setup separately:

For $2x - 7 = 3$:

For $2x - 7 = -3$:

These lead to two values of $x$; we will identify the matching choice next.

From $2x = 10$ and $2x = 4$, we find $x = 5$ and $x = 2$. The answer choices are $1$, $2$, $3$, and $4$. Among these, only $2$ is listed.

Therefore, the correct answer is 2.