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`