Question

Solve the following inequality and graph the solution.

a) (2|18 + 6x| < 0
b) (2|18 + 6x| > 0
c) (2|18 + 6x| ≤ 0
d) (2|18 + 6x| ≥ 0

Answer 1

To solve the inequality (2|18 + 6x| < 0), we need to consider two cases: Case 1: 18 + 6x < 0, Case 2: 18 + 6x > 0. The solution to the inequality is x < -3 or x > -3.

Step-by-step explanation:

To solve the inequality (2|18 + 6x| < 0), we need to consider two cases:

Case 1: 18 + 6x < 0

Solving this inequality gives x < -3.

Case 2: 18 + 6x > 0

Solving this inequality gives x > -3.

Therefore, the solution to the inequality is x < -3 or x > -3, which can be represented graphically as two separate intervals on the number line.