Question

solve: |4x + 10| < 10. state the solution set as an interval and graph the solution set. enter solutions as integers or reduced fractions. if there is no solution, type dne in the answer box and leave the graph blank.
a. the solution set as an interval is:

b. the graph of the solution set is:

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
clear all draw:

Explanation:

Step1: Rewrite absolute value inequality

$-10 < 4x + 10 < 10$

Step2: Subtract 10 from all parts

$-10 - 10 < 4x + 10 - 10 < 10 - 10$
$-20 < 4x < 0$

Step3: Divide by 4 on all parts

$\frac{-20}{4} < \frac{4x}{4} < \frac{0}{4}$
$-5 < x < 0$

Answer:

A. The solution set as an interval is: $(-5, 0)$
B. The graph of the solution set is:

• Draw an open circle at $x=-5$ and $x=0$ on the number line.
• Draw a solid line segment connecting these two open circles to represent all values between -5 and 0.