Answered

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

Sagot :

Given:

The compound inequality is

[tex]9<3x+6\leq 15[/tex]

To find:

The solution for the given compound inequality in interval notation.

Solution:

We have,

[tex]9<3x+6\leq 15[/tex]

Subtracting 6 from each side, we get

[tex]9-6<3x+6-6\leq 15-6[/tex]

[tex]3<3x\leq 9[/tex]

Divide each side by 3.

[tex]\dfrac{3}{3}<\dfrac{3x}{3}\leq \dfrac{9}{3}[/tex]

[tex]1<x\leq 3[/tex]

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].

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