What is the solution set of the compound inequality 8< 4 - x <10

-6 < x < - 4

Step-by-step explanation:

8 < 4 - x < 10

Split this up into 2 inequalities:

4 - x > 8

-x > 8 - 4

-x > 4 Divide both sides by - 1

x < - 4 (Note that sign flips when dividing by a negative).

Also 4 - x < 10

-x < 6

x > - 6

So the solution is - 6 < x < - 4

You can solve all together or separate.

so you do

8<4-x. subtract

-4 - 4

4<-x divide

-1. - 1

4>x

-4>x since you divide by negative the sign flips.

4-x<10

-4. - 4

-x<6

-1 - 1

x>-6

8<4-x<10

-4 - 4. - 4 subtract 4 on all 3

4<-x<6 divide - 1 to all 3

-4>x>-6 you flip sign since you divide by negative.

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