# How do you solve abs(3x-1)=14?

Jan 26, 2017

The solutions are $S = \left\{- \frac{13}{3} , 5\right\}$

#### Explanation:

$3 x - 1 = 14$

$3 x = 14 + 1 = 15$

$x = 5$

$- 3 x + 1 = 14$

$3 x = - 14 + 1 = - 13$

$x = - \frac{13}{3}$

Jan 26, 2017

See the entire solution process below:

#### Explanation:

The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore, you need to solve the term within the absolute value for both the negative and positive of what it is equated to giving two answers.

Solution 1)

$3 x - 1 = - 14$

$3 x - 1 + \textcolor{red}{1} = - 14 + \textcolor{red}{1}$

$3 x - 0 = - 13$

$3 x = - 13$

$\frac{3 x}{\textcolor{red}{3}} = - \frac{13}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = - \frac{13}{3}$

$x = - \frac{13}{3}$

Solution 2)

$3 x - 1 = 14$

$3 x - 1 + \textcolor{red}{1} = 14 + \textcolor{red}{1}$

$3 x - 0 = 15$

$3 x = 15$

$\frac{3 x}{\textcolor{red}{3}} = \frac{15}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = 5$

$x = 5$

The solution to this problem is:

$x = - \frac{13}{3}$ and $x = 5$

Jan 26, 2017

$x = - \frac{13}{3} \text{ or } x = 5$

#### Explanation:

There are 2 solutions to equations involving the $\textcolor{b l u e}{\text{absolute value}}$

$\Rightarrow 3 x - 1 = \textcolor{red}{\pm} 14$

$\textcolor{b l u e}{\text{Solution 1}}$

$3 x - 1 = 14$

$3 x \cancel{- 1} \cancel{+ 1} = 14 + 1$

$\Rightarrow 3 x = 15 \Rightarrow x = 5$

$\textcolor{b l u e}{\text{Solution 2}}$

$3 x - 1 = - 14$

$3 x \cancel{- 1} \cancel{+ 1} = - 14 + 1$

$\Rightarrow 3 x = - 13 \Rightarrow x = - \frac{13}{3}$

$\textcolor{b l u e}{\text{As a check}}$

"left side "=|(3xx5)-1|=|15-1|=|14|=14color(white)(xx)✔︎

"left side "=|(cancel(3^1)xx-13/cancel(3)^1)-1|=|-14|=14color(white)(xx)✔︎

$\Rightarrow x = 5 \text{ or " x=-13/3" are the solutions}$