Solve 3x - 4 ≤ 2 and 2x + 11 ≥ -1.

Solution:

Given 3x - 4 ≤ 2 and 2x + 11 ≥ -1

To solve, we must take x term to one side of the inequality

Consider first inequality 3x - 4 ≤ 2

Add 4 on both sides, we get 3x - 4 + 4 ≤ 2 + 4 ⇒ 3x ≤ 6

Divide with 3 on both sides, we get x ≤ 2 ---> [a]

Consider second inequality 2x + 11 ≥ -1

Subtract 11 on both sides, we get 2x + 11 - 11 ≥ -1 - 11 ⇒ 2x ≥ -12

Divide with 2 on both sides, we get ⇒ x ≥ -6 ---> [b]

From (a) and (b), we conclude that the solution lies between -6 and 2

Hence, the range is -6 ≤ x ≤ 2

Solve 3x - 4 ≤ 2 and 2x + 11 ≥ -1.

Summary:

By solving 3x - 4 ≤ 2 and 2x + 11 ≥ -1, we get solutions which lie between -6 ≤ x ≤ 2.