Question

An absolute value inequality is shown below.

2[x+31−4]<−8 Which set describes all solutions to the inequality?

A) x<−42
B) x>−18
C) 18D) x<−18 or x>−42

Answer 1

To solve the absolute value inequality 2|x+31-4| < -8, divide both sides by 2 and split the inequality into two cases. Solve each case separately and combine the solutions to find the solution set. The correct set is x < -31 or x > -23.

Step-by-step explanation:

The absolute value inequality given is 2|x+31-4| < -8.

To solve this inequality, begin by isolating the absolute value expression by dividing both sides by 2, giving |x+31-4| < -4.

Next, split the inequality into two cases: x+31-4 < -4 and x+31-4 > 4.

Solving the first case, x+31-4 < -4, we can simplify to x+31 < 0, and then x < -31.

For the second case, x+31-4 > 4, we can simplify to x+31 > 8, and then x > -23.

Therefore, the solution set for the original inequality is x < -31 or x > -23, which is represented by option D) x < -18 or x > -42.