# How do you graph and solve  |2x-5| >= -1?

Mar 20, 2016

Just find when $2 x - 5$ is negative and put a negative sign to "make" it positive for the absolute part. Answer is:

$| 2 x - 5 | > - 1$ for every $x \in \mathbb{R}$

They are never equal.

#### Explanation:

Quick solution

The left part of the equation is an absolute, so it is always positive with a minimum of 0. Therefore, the left part is always:

$| 2 x - 5 | \ge 0 > - 1$

$| 2 x - 5 | > - 1$ for every $x \in \mathbb{R}$

Graph solution

$| 2 x - 5 |$

This is negative when:

$2 x - 5 < 0$

$2 x < 5$

$x < \frac{5}{2}$

And positive when:

$2 x - 5 > 0$

$2 x > 5$

$x > \frac{5}{2}$

Therefore, for you must graph:

$- \left(2 x - 5\right) = - 2 x + 5$ for $x < \frac{5}{2}$

$2 x - 5$ for $x > \frac{5}{2}$

These are both lines. Graph is:

graph{|2x-5| [-0.426, 5.049, -1.618, 1.12]}

As we can clearly see, the graph never passes through $- 1$ so the equal part is never true. However, it is always greater than $- 1$ so the answer is:

For every $x \in \mathbb{R}$ (which means $x \in \left(- \infty , + \infty\right)$