# How do you solve 2|1/3s-5| + 3=8?

Feb 8, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the absolute value term while keeping the equation balanced:

$2 \left\mid \frac{1}{3} s - 5 \right\mid + 3 - \textcolor{red}{3} = 8 - \textcolor{red}{3}$

$2 \left\mid \frac{1}{3} s - 5 \right\mid + 0 = 5$

$2 \left\mid \frac{1}{3} s - 5 \right\mid = 5$

Next, divide each side of the equation by $\textcolor{red}{2}$ to isolate the absolute value function while keeping the equation balanced:

$\frac{2 \left\mid \frac{1}{3} s - 5 \right\mid}{\textcolor{red}{2}} = \frac{5}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left\mid \frac{1}{3} s - 5 \right\mid}{\cancel{\textcolor{red}{2}}} = \frac{5}{2}$

$\left\mid \frac{1}{3} s - 5 \right\mid = \frac{5}{2}$

The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore we must solve the term in the absolute value function for both its negative and positive form.

Solution 1)

$\frac{1}{3} s - 5 = - \frac{5}{2}$

$\frac{1}{3} s - 5 + \textcolor{red}{5} = - \frac{5}{2} + \textcolor{red}{5}$

$\frac{1}{3} s - 0 = - \frac{5}{2} + \left(\frac{2}{2} \times \textcolor{red}{5}\right)$

$\frac{1}{3} s = - \frac{5}{2} + \frac{10}{2}$

$\frac{1}{3} s = \frac{5}{2}$

$\textcolor{red}{3} \times \frac{1}{3} s = \textcolor{red}{3} \times \frac{5}{2}$

$\cancel{\textcolor{red}{3}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} s = \frac{15}{2}$

$s = \frac{15}{2}$

Solution 2)

$\frac{1}{3} s - 5 = \frac{5}{2}$

$\frac{1}{3} s - 5 + \textcolor{red}{5} = \frac{5}{2} + \textcolor{red}{5}$

$\frac{1}{3} s - 0 = \frac{5}{2} + \left(\frac{2}{2} \times \textcolor{red}{5}\right)$

$\frac{1}{3} s = \frac{5}{2} + \frac{10}{2}$

$\frac{1}{3} s = \frac{15}{2}$

$\textcolor{red}{3} \times \frac{1}{3} s = \textcolor{red}{3} \times \frac{15}{2}$

$\cancel{\textcolor{red}{3}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} s = \frac{45}{2}$

$s = \frac{45}{2}$

The solutions is: $s = \frac{15}{2}$ and $s = \frac{45}{2}$