Solve the compound inequality and graph the solutions.

−3 < x - 10/ 4 < -2

The solution to the inequality may be obtained as follows:

|

3

x

−

4

|

+

6

<

10

|

3

x

−

4

|

<

4

[

Subtract 6 from both sides

]

The expression inside the absolute value sign can either be a positive or a negative value.

For positive value:

(

3

x

−

4

)

<

4

3

x

<

8

[

Add 4 to both sides

]

x

<

8

3

[

Divide both sides by 3

]

For negative value:

−

(

3

x

−

4

)

<

4

−

3

x

+

4

<

4

−

3

x

<

0

[

Subtract 4 from both sides

]

x

>

0

[

Divide both sides by -3 and flip the inequality sign

Step-by-step explanation:

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