Compound inequalities

Question

The inequality 2x + 3 ≤ x + 10 ≤ 3x + 3 means that x is in the closed interval [A, B] where A is and B is:

Answer 1

First, we focus on the right-hand inequalities by subtracting 3x from each:

-x+3 <= -2x+10 <= 3.

Solving the right side: -2x+10 <= 3 implies -2x<=-7 implies x>=7/2.

Next, we focus on the left-hand inequality: -x+3 <= -2x+10 implies x+3 <= 10 implies x <= 7.

Therefore, (7/2) <= x <= 7, A = (7/2), B = 7.