Question

Solve each compound inequality for x, and graph the solution on a number line.

a. 9 + 2x < 17 or 7 - 4x < -9
b. 6 ≤ x/2 ≤ 11

Answer 1

a) x < 4 or x > 4

b) 12 ≤ x ≤ 22

Explanation:

a) 9 + 2 x < 17 or 7 - 4x < -9

First we will solve the first part:

9 + 2x < 17

2x < 17 - 9

2x < 8

x < 4

and the second one will be:

7 - 4x < -9

-4x < -9 -7

-4x < -16

4x > 16

x > 4

Therefore, x < 4 or x > 4. In a number line (below) this solution will be all the real numbers but 4.

b) 6 ≤ x/2 ≤ 11

We will solve the first one:

6≤ x/2

12 ≤ x

And the second part:

x/2≤ 11

x≤22

So the solution will be 12 ≤ x ≤ 22 and in the number line it will look as the numbers from 12 to 22 (including them)