Question

How do you solve and graph `-23<=2x - 1<=1`?

Answer 1

`-11 <= x <= 1`

Explanation:

Work out the two sides of the inequality separately:

`-23<=2x -1 <=1`

`-23<=2x -1 " and "2x -1 <=1`
On the left, keep the x on the right. On the right keep it on the left.

`-23+1 <=2x " " 2x <= 1+1`
`-" "22 <=2x " " 2x <=2`
`" "-11 <= x " " x <= 1`

The two x terms are the same x, so combine them into one inequality:

`-11 <= x <= 1`

To graph it:

On a number line graph there will be a closed circle on -11 and a closed circle on 2, because both of these values are INCLUDED in the solution. Draw a line between the two circles to indicate that `x` can be any Real number between them.