# How do you solve and write the following in interval notation: |6t-6|<6?

Jan 9, 2017

See full solution process below

#### Explanation:

Because this is a problem contain the absolute value function we must solve the problem for both the negative and positive forms of the problem or in this case +6 and -6.

Also, because it is an inequality we must solve it as a system of inequalities as shown below.

We can rewrite this problem as:

$- 6 < 6 t - 6 < 6$

We can now solve while ensuring we perform all operations to each portion of the system of inequalities.

First we will add $\textcolor{red}{6}$ to each portion of the system:

$- 6 + \textcolor{red}{6} < 6 t - 6 + \textcolor{red}{6} < 6 + \textcolor{red}{6}$

$0 < 6 t - 0 < 12$

$0 < 6 t < 12$

Next we will divide each portion of the system by $\textcolor{red}{6}$ to solve for $t$ while keeping the system balanced:

$\frac{0}{\textcolor{red}{6}} < \frac{6 t}{\textcolor{red}{6}} < \frac{12}{\textcolor{red}{6}}$

$0 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} t}{\cancel{\textcolor{red}{6}}} < 2$

$0 < t < 2$

Writing this solution in interval form gives:

(0, 2)