How do you solve |x - 7| <10?

Jan 26, 2017

See the entire solution process below:

Explanation:

To solve an absolute value inequality you must solve for both the negative and positive form of what the term within the absolute value function is compared to using a complex inequality.

$\left\mid x - 7 \right\mid < 10 \to$

$- 10 < x - 7 < 10$

Now, add $\textcolor{red}{7}$ to each section of the complex inequality to solve for $x$ while keeping the inequality balanced:

$- 10 + \textcolor{red}{7} < x - 7 + \textcolor{red}{7} < 10 + \textcolor{red}{7}$

$- 3 < x - 0 < 17$

$- 3 < x < 17$

Or, in interval form:

(-3, 17)