# How do you solve the equation abs(3(x-2))=10?

Nov 29, 2017

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:

$\textcolor{red}{3} \left(x - 2\right) = - 10$

$\left(\textcolor{red}{3} \times x\right) - \left(\textcolor{red}{3} \times 2\right) = - 10$

$3 x - 6 = - 10$

$3 x - 6 + \textcolor{red}{6} = - 10 + \textcolor{red}{6}$

$3 x - 0 = - 4$

$3 x = - 4$

$\frac{3 x}{\textcolor{red}{3}} = - \frac{4}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = - \frac{4}{3}$

$x = - \frac{4}{3}$

Solution 1:

$\textcolor{red}{3} \left(x - 2\right) = 10$

$\left(\textcolor{red}{3} \times x\right) - \left(\textcolor{red}{3} \times 2\right) = 10$

$3 x - 6 = 10$

$3 x - 6 + \textcolor{red}{6} = 10 + \textcolor{red}{6}$

$3 x - 0 = 16$

$3 x = 16$

$\frac{3 x}{\textcolor{red}{3}} = \frac{16}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = \frac{16}{3}$

$x = \frac{16}{3}$

The Solution Is: $x = \left\{- \frac{4}{3} , \frac{16}{3}\right\}$