# How do you solve and write the following in interval notation: -5<5+2x<11?

Jun 17, 2016

$x \in \left(- 5 , 3\right)$

#### Explanation:

You can add/subtract both sides of an inequality without changing the orientation of the inequality;
you can also multiply or divide both (all) sides of an inequality by a value greater than zero without changing the orientation of the inequality..

Given: #-5 < 5 +2x <11

subtract $5$ from each "side
$- 10 < 2 x < 6$

divide each "side" by $2$
$- 5 < x < 3$

Jun 17, 2016

$- 5 < x < 3$ or in interval notation: $x \in \left(- 5 , 3\right)$

#### Explanation:

Break the question into two inequalities and solve each separately.

LHS: keep x term on the right but on the RHS keep x term on left

$- 5 < 5 + 2 x \text{ and } 5 + 2 x < 11$

$- 5 - 5 < 2 x \text{ } 2 x < 11 - 5$

$- 10 < 2 x \text{ } 2 x < 6$

$- 5 < x \text{ } x < 3$

But the x terms are the same term, so the two parts can be combined:

$- 5 < x < 3$