# How do you solve abs(7x+1/8 )=2?

Mar 20, 2018

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.

Solution 1:

$7 x + \frac{1}{8} = - 2$

$7 x + \frac{1}{8} - \textcolor{red}{\frac{1}{8}} = - 2 - \textcolor{red}{\frac{1}{8}}$

$7 x + 0 = \left(\frac{8}{8} \times - 2\right) - \textcolor{red}{\frac{1}{8}}$

$7 x = - \frac{16}{8} - \textcolor{red}{\frac{1}{8}}$

$7 x = - \frac{17}{8}$

$\textcolor{red}{\frac{1}{7}} \times 7 x = \textcolor{red}{\frac{1}{7}} \times - \frac{17}{8}$

$\frac{7}{\textcolor{red}{7}} x = - \frac{17}{56}$

$1 x = - \frac{17}{56}$

$x = - \frac{17}{56}$

Solution 2:

$7 x + \frac{1}{8} = 2$

$7 x + \frac{1}{8} - \textcolor{red}{\frac{1}{8}} = 2 - \textcolor{red}{\frac{1}{8}}$

$7 x + 0 = \left(\frac{8}{8} \times 2\right) - \textcolor{red}{\frac{1}{8}}$

$7 x = \frac{16}{8} - \textcolor{red}{\frac{1}{8}}$

$7 x = \frac{15}{8}$

$\textcolor{red}{\frac{1}{7}} \times 7 x = \textcolor{red}{\frac{1}{7}} \times \frac{15}{8}$

$\frac{7}{\textcolor{red}{7}} x = \frac{15}{56}$

$1 x = \frac{15}{56}$

$x = \frac{15}{56}$

The Solution Set Is: $x = \left\{- \frac{17}{56} , \frac{15}{56}\right\}$