# How do you solve and graph abs(2z-9)<=1?

Sep 20, 2017

Find the two values of $z$ where the equation $| 2 z - 9 | = 1$ is true.
The inequality will be true for those values and all values in between.

#### Explanation:

Solve: $| 2 z - 9 | = 1$

Separate into two equations:

$2 z - 9 = 1$ and $- \left(2 z - 9\right) = 1$

Multiply both sides of the second equation by -1:

$2 z - 9 = 1$ and $2 z - 9 = - 1$

Add 9 to both sides of both equations:

$2 z = 10$ and $2 z = 8$

Divide both sides of both equations by 2:

$z = 5$ and $z = 4$

The inequality will be true between these values:

$4 \le z \le 5$

Sep 20, 2017

z=4, z=5

#### Explanation:

$| 2 z - 9 | \le 1$ gives two equations
1. $\left(2 z - 9\right) \le 1$
$\implies 2 z \le 10$
$\implies z \le 5$
2. $- \left(2 z - 9\right) \le 1$
$\implies - 2 z + 9 \le 1$
$\implies - 2 z \le - 8$
$\implies 2 z \ge 8$
$\implies z \ge 4$

So Values of z
$z = 4 , z = 5$

in Graph there are two lines z=4 and z=5