Question

Which absolute value inequality has -7 and 4 as two of its solutions?

A. |x| - 3 ≤ 30
B. |−7x| ≥ 49

Answer 1

The absolute value inequality that has -7 and 4 as two of its solutions is |−7x| ≥ 49. We need to solve for x by isolating the absolute value and considering both possibilities for the signs. The solutions are x ≤ -7 or x ≥ 7.

Step-by-step explanation:

The absolute value inequality that has -7 and 4 as two of its solutions is option B, |−7x| ≥ 49. In this inequality, we need to solve for x in order to find the range of values that satisfy the inequality. Let's solve it step by step:

1. Start by isolating the absolute value expression: |−7x| ≥ 49.
2. The inequality |−7x| ≥ 49 can be rewritten as -7x ≥ 49 or 7x ≥ 49, depending on the sign of −7x. Since it is an absolute value inequality, we need to consider both possibilities.
3. For -7x ≥ 49, divide both sides by -7. This gives us x ≤ -7.
4. For 7x ≥ 49, divide both sides by 7. This gives us x ≥ 7.
5. Combining both solutions, we have x ≤ -7 or x ≥ 7.

Therefore, the absolute value inequality that has -7 and 4 as two of its solutions is |−7x| ≥ 49.