# How do you solve and graph abs(u+3)<7?

Dec 3, 2017

Solution: $\textcolor{g r e e n}{- 10 < u < 4}$

Using interval notations our solution can be written as

color(green)((-10, 4)

#### Explanation:

We are given the inequality

$\textcolor{b l u e}{| u + 3 | < 7}$

Absolute Inequalities yield two values, one with positive sign and the other with the negative sign.

Hence,

We will rewrite this inequality as

$\textcolor{b l u e}{- 7 < u + 3 < + 7}$

The above inequality has three parts:

$- 7 , u + 3 , \mathmr{and} + 7$

We can solve this inequality by subtracting $3$ from all the three parts of the inequality.

So, we get,

$\textcolor{b l u e}{- 7 - 3 < u + 3 - 3 < + 7 - 3}$

$\textcolor{g r e e n}{\Rightarrow - 10 < u < 4}$

Using interval notations our solution can be written as

color(green)((-10, 4)