How do you solve and graph $- 5 < 2 x + 1 < 4$ $-5 < 2x + 1 < 4$ ?

Question

2023 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-02T10:11:27

$- 3 < x < \frac{3}{2}$ $-3< x<3/2$

Shade the area between a dashed line for $x = - 3$ $x=-3$ and a dashed line for $x = \frac{3}{2}$ $x=3/2$

We want just $x$ $x$ on its own in the middle.

First,we take away 1 from both sides:

$- 5 - 1 < 2 x + 1 - 1 < 4 - 1$ $-5-1<2x+1-1<4-1$
$- 6 < 2 x < 3$ $-6<2x<3$

Then divide all terms by $2$ $2$ :

$- \frac{6}{2} < \frac{2 x}{2} < \frac{3}{2}$ $-6/2<(2x)/2<3/2$
$- 3 < x < \frac{3}{2}$ $-3< x<3/2$

To graph the inequality, draw a dashed line for $x = - 3$ $x=-3$ and $x = \frac{3}{2}$ $x=3/2$ and shade between the two lines.

How do you solve and graph −5<2x+1<4-5 < 2x + 1 < 4?