Question

Solve for x: 12x + 28 < -56 OR 18x + 30 ≤ -24

1. (7, ∞)
2. (- ∞, 10)
3. (- ∞, - 3]
4. (- ∞, 7)
5. None of these

Answer 1

Correct Answer - Option 3 : (- ∞, - 3]

Solving equation 1:

12x + 28 < −56

12x < - 56 - 28

12x < - 84

12x < - 84

x < - 7

So,

\(x \in (-\infty,-7)\)      ----(1)

Solving equation 2:

18x + 30 ≤ −24

18x ≤ −24 - 30

18x ≤ −54

x ≤ −3

xϵ(- ∞, - 3)      ----(2)

From equation (1) and equation (2)

x ϵ (- ∞, -3]