# Three-part inequalities

## Divide or multiply by negatives

The same rules apply to three part inequalities with regard to dividing or multiplying by a negative you flip both inequality signs.

Examples

1.  Solve the following three-part inequality

-5<=3\-2x<=5

Subtract -3  from all 3 sides to try and get x on its own.

-5-3<=3-3-2x<=5-3

-8<=-2x<=2

Divide all 3 sides by -2  to get x on its own but you must flip the inequality sign too:

(-8)/-2>=\(-2x)/-2>=2/-2

4>=x>=-1

Answer: 4  is greater than or equal to x and x is greater than or equal to -1.

2.  Solve

10>(2x-5)/-4>5

Multiply all the sides by -4  to get x on its own. Don’t forget to flip the inequality sign.

-4times10<(-4times(2x-5))/-4<-4times5

-40<2x-5<-20

Add 5  to each side to get x on its own.

-40+5<2x-5+5<-20+5

-35<2x<-15

Divide all three sides by 2  to get x on its own.

(-35)/2<(2x)/2<-15/2

-17 1/2<\x<-7\1/2