An absolute value inequality is shown below.

Question

-214x - 61 + 7 > -5
Which set describes all solutions to the inequality?
Empty set, D
B
x≤ 0 or x≥ 3
x ≥ 0 or x ≤ 3
All real numbers, *

Answer 1

To solve the absolute value inequality, we can start by isolating the absolute value term:

-214x - 61 + 7 > -5
-214x - 54 > -5

Next, we can add 54 to both sides:

-214x > 49

Then, divide both sides by -214. Since we divide by a negative number, we need to reverse the inequality sign:

x < 49/-214
x < -0.227

The solution to the absolute value inequality is all real numbers less than -0.227, which is represented by the set of all real numbers, *.