Question

Solve the inequality 2 |6x - 7| + 12 ≤ 22

a) x ≤ 2 and x ≥ 1/3
b) x ≤ 1 and x ≥ 2/3
c) x ≤ 1/3 and x ≥ 2
d) x ≤ 2/3 and x ≥ 1

Answer 1

To solve the inequality 2 |6x - 7| + 12 ≤ 22, subtract 12 from both sides, divide both sides by 2, split the inequality into two separate inequalities, and simplify to find x ≤ 2 and x ≥ 1/3.

Step-by-step explanation:

To solve the inequality 2 |6x - 7| + 12 ≤ 22, we can start by subtracting 12 from both sides:

2 |6x - 7| ≤ 10

Next, we can divide both sides by 2:

|6x - 7| ≤ 5

Now we can split the inequality into two separate inequalities:

1. 6x - 7 ≤ 5
2. -(6x - 7) ≤ 5

Simplifying each inequality:

1. 6x ≤ 12 → x ≤ 2
2. -6x + 7 ≤ 5 → x ≥ 1/3

Therefore, the solution to the inequality is x ≤ 2 and x ≥ 1/3, which corresponds to option a) in the given choices.