# How do you graph and solve abs (x -7) <=4?

Jul 30, 2018

#### Answer:

See a solution process below:

#### Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Therefore we can rewrite this problem as a system of inequalities and solve it as:

$- 4 \le x - 7 \le 4$

$- 4 + \textcolor{red}{7} \le x - 7 + \textcolor{red}{7} \le 4 + \textcolor{red}{7}$

$3 \le x - 0 \le 11$

$3 \le x \le 11$

Or

$x \ge 3$; $x \le 11$

Or, in interval notation:

$\left[3 , 11\right]$