Question

Find the set of the solutions for each of the following Absolute Value Inequalities.

A. |1 - 3/4k| ≥ 7: k ≥ 4/3
B. |1 - 3/4k| ≥ 7: k ≤ -4/3
C. |1 - 3/4k| ≥ 7: k ≥ -4/3
D. |1 - 3/4k| ≥ 7: k ≤ 4/3

Answer 1

To solve the absolute value inequality |1 - (3/4)k| ≥ 7, we isolate the absolute value expression and consider two cases: one where the expression inside the absolute value is positive and one where it is negative.

Step-by-step explanation:

To solve the absolute value inequality |1 - (3/4)k| ≥ 7, we need to isolate the absolute value expression and consider two cases: one where the expression inside the absolute value is positive and one where it is negative.

1. If 1 - (3/4)k ≥ 0, we can remove the absolute value signs and solve for k:

• 1 - (3/4)k ≥ 7
• - (3/4)k ≥ 6
• k ≤ -8

If 1 - (3/4)k < 0, we need to change the direction of the inequality when removing the absolute value signs:

• -(1 - (3/4)k) ≥ 7
• -(1 - (3/4)k) ≥ 7
• k ≥ 4/3

Therefore, the solutions for the absolute value inequality are:

k ≤ -8 or k ≥ 4/3.