Question

How do you solve and graph the compound inequality `2x+5<=11` and `4(x-1)+12>=0`?

Answer 1

Solve system of linear equations in one variable:
2x + 5 <= 11
4(x - 1) + 12 >= 0

Explanation:

(1) `2x + 5 <= 11 --> 2x <= 6 --> x <= 3`

(2) `4x - 4 + 12 >= 0 --> 4x >= - 8 --> x >= - 2`

------------|-2======|0===========|3--------------

Answer: closed interval [-2, 3]. The 2 critical points (-2) and (3) are included in the solution set.