Solve the inequality |2x - 5| ≤ 9.

• A. -3 ≤ x ≤ 6
• B. x ≤ -2 or x ≥ 7
• C. -2 ≤ x ≤ 7
• D. -7 ≤ x ≤ 2

Answer: (C)

When an absolute value is constrained by a "less than or equal" bound, the inside must lie between the negative and positive of that bound. In other words, |something| ≤ 9 means -9 ≤ something ≤ 9.

Apply that to the inside: -9 ≤ 2x - 5 ≤ 9. Add 5 to every part to isolate the term with x: -4 ≤ 2x ≤ 14. Divide by 2: -2 ≤ x ≤ 7.

So the values of x that satisfy the inequality are all numbers from -2 up to 7, inclusive. The interval -2 ≤ x ≤ 7 is the correct solution. The other ranges either exceed this band or miss part of it, so they don’t satisfy the inequality.