Question

Which compound inequality has no solution?

x + 5 < 5 and StartFraction 1 over 3 EndFraction x plus 5 less than 5 and StartFraction 2 x plus 1 over 3 EndFraction greater than 1. > 1
3(x + 4) < 12 or 3x + 1 > 10
10 < 3(x – 2) + 1 or 10 less than 2 left-parenthesis x minus 2 right-parenthesis plus 1 or StartFraction 2 x plus 1 over 3 EndFraction less than 2. < 2
11 ≤ 5(x + 3) – 9 and 5(x + 3) – 9 < 21

Answer 1

The first compound inequality has no solution.

Interpret it as:
x + 5 < 5 and (1/3)(x + 5) < 5 and (2x + 1)/3 > 1.

Solve each:
- x + 5 < 5 → x < 0
- (1/3)(x + 5) < 5 → x + 5 < 15 → x < 10 (redundant)
- (2x + 1)/3 > 1 → 2x + 1 > 3 → x > 1

You would need x < 0 and x > 1 at the same time, which is impossible, so there is no solution.