# How do you solve and graph -9 <=2x-5 and 2x +1 < 5?

Nov 21, 2017

solve:
$- 2 \le x < 2$

graph (reds):
$- - - - - \textcolor{red}{\left(- 2\right) - - 0 - -} 2 - - - - - - - \to x$

#### Explanation:

$- 9 \le 2 x - 5$
$2 x + 1 < 5$
$\implies$
$- 9 \le 2 x - 5$
$2 x - 5 < - 1$
$\implies$
$- 9 \le 2 x - 5 < - 1$
$\implies$
$- 4 \le 2 x < 4$
$\implies$
$- 2 \le x < 2$

on x axis:
$- - - - - - - 0 - - - - - - - - - \to x$

we put $x = - 2 , x = 2$
$\implies$
$- - - - - \left(- 2\right) - - 0 - - 2 - - - - - - - \to x$

we want $x \ge - 2 \mathmr{and} x < 2$ (paints in red)
$\implies$
$- - - - - \textcolor{red}{\left(- 2\right) - - 0 - -} 2 - - - - - - - \to x$
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