# How do you solve abs(5-m)<1?

Mar 20, 2017

See the entire solution process below:

#### Explanation:

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

We create a system of inequalities to solve this:

$- 1 < 5 - m < 1$

First, subtract $\textcolor{red}{5}$ from each segment of the system to isolate the $m$ term while keeping the system of inequalities balanced:

$- \textcolor{red}{5} - 1 < - \textcolor{red}{5} + 5 - m < - \textcolor{red}{5} + 1$

$- 6 < 0 - m < - 4$

$- 6 < - m < - 4$

Now, multiply each segment by $\textcolor{b l u e}{- 1}$ t solve for $m$ while keeping the system of inequalities balanced. However, because we are multiplying or dividing inequalities by a negative term we must reverse the inequality operators:

$\textcolor{b l u e}{- 1} \times - 6 \textcolor{red}{>} \textcolor{b l u e}{- 1} \times - m \textcolor{red}{>} \textcolor{b l u e}{- 1} \times - 4$

$6 \textcolor{red}{>} m \textcolor{red}{>} 4$