Question

solve the inequality. graph the solution.
|7x - 7| + 2 < 23

what is the solution?
( type an inequality or a compound inequality. )
choose the correct graph below.
a. graph with two blue dots
-10 -5 0 5 10
b. graph with two open circles and blue lines
-10 -5 0 5 10
c. graph with two open circles and blue line in the middle
-10 -5 0 5 10
d. graph with two blue dots and blue line in the middle
-10 -5 0 5 10

Explanation:

Step1: Isolate the absolute value

Subtract 2 from both sides.
$$|2x - 7| < 23 - 2$$
$$|2x - 7| < 21$$

Step2: Rewrite as compound inequality

For $|A| < b$, $-b < A < b$.
$$-21 < 2x - 7 < 21$$

Step3: Add 7 to all parts

Isolate the term with $x$.
$$-21 + 7 < 2x < 21 + 7$$
$$-14 < 2x < 28$$

Step4: Divide by 2

Solve for $x$.
$$\frac{-14}{2} < x < \frac{28}{2}$$
$$-7 < x < 14$$

Step5: Match to graph

Open circles at -7 and 14, shaded between them.

Answer:

The solution is $\boldsymbol{-7 < x < 14}$, which corresponds to Graph C.