Question

Solve the inequality. Give solution set in interval notation.

2x-11 < -3(x+2)

Answer 1

To solve the inequality 2x - 11 < -3(x + 2), distribute -3, combine like terms, and isolate x. This gives x < 1, and the solution set in interval notation is (-∞, 1).

Step-by-step explanation:

To solve the inequality 2x - 11 < -3(x + 2), first distribute the -3 on the right side of the inequality:

2x - 11 < -3x - 6

Next, move all terms involving x to one side and constant terms to the other side:

2x + 3x < -6 + 11

Combine like terms:

5x < 5

Now, divide both sides by 5 to isolate x:

x < 1

The solution set in interval notation is (-∞, 1).