Question

Which inequality describes all the solutions to 5(3 − x) < −2x + 6?

Answer 1

Given:

The inequality is

`5(3-x)<-2x+6`

To find:

The inequality that solution describes all the solutions to the given inequality.

Solution:

We have,

`5(3-x)<-2x+6`

Using distributive property, we get

`5(3)+5(-x)<-2x+6`

`15-5x<-2x+6`

`15-6<-2x+5x`

`9<3x`

Divide both sides by 3.

`(9)/(3)<x`

`3<x`

It can be written as

`x>3`

Therefore, the value of x is greater than 3. So, the required inequality is either
`x>3` or
`3<x`.