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

Jun 21, 2016

$- 11 \le x \le 1$

#### Explanation:

Work out the two sides of the inequality separately:

$- 23 \le 2 x - 1 \le 1$

$- 23 \le 2 x - 1 \text{ and } 2 x - 1 \le 1$
On the left, keep the x on the right. On the right keep it on the left.

$- 23 + 1 \le 2 x \text{ } 2 x \le 1 + 1$
$- \text{ "22 <=2x " } 2 x \le 2$
$\text{ "-11 <= x " } x \le 1$

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

$- 11 \le x \le 1$

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.