Question

Which of these inequalities are equivalent to r > -11? Check all that apply.
-r < 11
3r < -33
3r > -33
-3r < 33
-3r > 33

Answer 1

Solve each for r (remember: dividing or multiplying by a negative flips the inequality).

- -r < 11 → multiply by -1 (flip): r > -11 (equivalent)
- 3r < -33 → divide by 3: r < -11 (not equivalent)
- 3r > -33 → divide by 3: r > -11 (equivalent)
- -3r < 33 → divide by -3 (flip): r > -11 (equivalent)
- -3r > 33 → divide by -3 (flip): r < -11 (not equivalent)

Equivalent: -r < 11, 3r > -33, -3r < 33.