Question

How do you solve `-4/5(x-3)≤-12`?

Answer 1

`x >= 18`

Explanation:

Treat inequalities in exactly the same way as an equation unless you are are multiplying or dividing by a negative number. In this case the inequality sign has to change around.
Also do not cross-multiply across an inequality.

Let's get rid of the annoying fraction outside the bracket by multiplying by `5/4`, leaving the minus sign there for now.

`color(red)(5/4) xx-4/5(x-3)<= color(red)(5/4) xx-12`

`=-(x-3) <=-15 " Multiplying out gives"`

`" "=-x +3 <=-15`

The problem now is the `-x`. The easiest is to move it to the right side to make it positive ;

`15 + 3 <=x`

`18 <= x` which can also be written as `x >= 18`

The other method would involve dividing by -1.
`-x <=-15 -3`
`-x <=-18 " divide by -1 "rArr" sign will change"`

`x >= 18`