How do you solve the inequality 5x + 7 <2 and 5x + 7> –18?

Jan 2, 2016

$- 5 < x < - 1$

Explanation:

This can be rewritten as

$- 18 < 5 x + 7 < 2$

To solve this, isolate $x$. The first step will be subtracting $7$. However, subtract $7$ from all parts of the inequality.

$- 18 - 7 < 5 x + 7 - 7 < 2 - 7$

Which yields

$- 25 < 5 x < - 5$

Now, divide each part by $5$.

$- 5 < x < - 1$