Question

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

Answer 1

-6 < x < -4

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

Answer 2

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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