Which compound inequality has no solution?

x + 5 1

3 (x + 4) 10

10 < 3 (x - 2) + 1 or < 2

11 ≤ 5 (x + 3) - 9 and 5 (x + 3) - 9 < 21

Checking the compound inequalities the first one has no solution:

x + 5 1

Step-by-step explanation:

1) x+51

Subtracting 5 both sides of the inequality:

x+5-51

x1

Solution = (-Infinite, 0) ∩ (1, Infinite)

Solution = ∅ = { } (Empty set)

This compound inequality has no solution

2) 3 (x + 4) 10

3 (x) + 3 (4) 10-1

3x + 12 9

3x + 12-12 9/3

3x 3

3x/3 3

x 3

Solution = (-Infinite, 0) U (3, Infinite)

3) 10 < 3 (x - 2) + 1 or < 2

10 < 3 (x) - 3 (2) + 1 or < 2

10 < 3x - 6 + 1 or < 2

10 < 3x - 5 or < 2

10+5 < 3x - 5+5 or < 2

15 < 3x or < 2

15/3 < 3x/3 or < 2

5 < x or < 2

x>5 or <2

Solution = (5, Infinite) U (-Infinite, 2)

Solution = (-Infinite, 2) U (5, Infinite)

4) 11 ≤ 5 (x + 3) - 9 and 5 (x + 3) - 9 < 21

11 ≤ 5 (x) + 5 (3) - 9 and 5 (x) + 5 (3) - 9 < 21

11 ≤ 5x + 15 - 9 and 5x + 15 - 9 < 21

11 ≤ 5x + 6 and 5x + 6 < 21

11 - 6 ≤ 5x + 6 - 6 and 5x + 6 - 6 < 21 - 6

5 ≤ 5x and 5x < 15

5/5 ≤ 5x/5 and 5x/5 < 15/5

1 ≤ x and x < 3

x ≥ 1 and x < 3

Solution = [1, Infinite) ∩ (-Infinite, 3)

Solution = [1, 3)

Answer:Checking the compound inequalities the first one has no solution:

x + 5 1