# Two-part inequalities

## Divide or multiply by negatives

Examples

1.  Solve

-12x<=4

Divide both sides by -12  to get x on its own.

(-12x)/-12>=(4)/-12

x>=-(1)/3

(Notice how we reversed the inequality)

2.  Solve

11-2x>=3x+16

Take 11  from both sides

-11+11-2x>=3x+16-11

-2x>=3x+16-11

-2x>=3x+5

Take 3x from both sides

-2x-3x>=3x-3x+5

-5x>=5

DIVIDE BY -5   (careful)

(-5x)/-5<=(5)/-5

x<=-1

(Notice how we reversed the inequality)

3.  Solve

-2(4x +1)<10

Start by multiplying out using BIDMAS

Therefore

-2times4x+(-2)times1<10

-8x-2<10

-8x<12

Divide by -8  to get x on its own. But don’t forget to flip the sign.

(-8x)/-8>(12)/-8

x>\-12/8

And now simplify the fraction

x>\-3/2

x>\-1\1/2

4.  Solve

(2x-5)/-4>5

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

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

2x-5<-20

Add 5  to both sides to get x on its own.

2x-5+5<-20+5

2x<-15

Divide both sides by 2  to get x on its own.

(2x)/2<-15/2

x<\-7\1/2