Answer:
Checking the compound inequalities the first one has no solution:
x + 5 < 5 and > 1
Explanation:
1) x+5<5 and >1
Subtracting 5 both sides of the inequality:
x+5-5<5-5 and >1
x<0 and >1
Solution = (-Infinite, 0) ∩ (1, Infinite)
Solution = ∅ = { } (Empty set)
This compound inequality has no solution
2) 3(x + 4) < 12 or 3x + 1 > 10
3(x) +3(4) < 12 or 3x + 1-1 > 10-1
3x +12 < 12 or 3x > 9
3x +12-12 < 12-12 or 3x/3 > 9/3
3x < 0 or x > 3
3x/3 < 0/3 or x > 3
x < 0 or 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)