Question

How do you solve `-4x-8<=56`?

Answer 1

`-4x-8<=56`
or
`4x+8>=-56`
or
`4(x+2)>=-56`
or
`x+2>=-56/4`
or
`x+2>=-14`
or
`x>=-14-2`
or
`x>=-16`

Answer 2

`x>= -16`

Explanation:

Treat an inequality in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign must change around.

We can tackle this question in 2 ways: Compare them.

Make the x-term positive`color(white)(.......................)`keep the x-term on left

`-4x -8 <= 56color(white)(...................................)-4x -8 <= 56`

`-8-56 <= 4xcolor(white)(.........................................)-4x <=56+8`

`-64 <= 4x " "div 4color(white)(....................................)-4x <=64"`

`-16 <= xcolor(white)(..................................................) (-4x)/(-4) color(red)(>=) 64/(-4)`

`x>= -16color(white)(.......................................................)x>= -16`