Question

Question

Solve 9 < 3x + 6< = 15 and write the solution in interval notation. If there is no solution, type Ø.

Answer 1

Given:

The compound inequality is

`9<3x+6\leq 15`

To find:

The solution for the given compound inequality in interval notation.

Solution:

We have,

`9<3x+6\leq 15`

Subtracting 6 from each side, we get

`9-6<3x+6-6\leq 15-6`

`3<3x\leq 9`

Divide each side by 3.

`(3)/(3)<(3x)/(3)\leq (9)/(3)`

`1<x\leq 3`

Here, 1 is not included in the solution set and 3 is included in the solution set.

Therefore, the solution in interval notation is (1,3].