# How do you solve abs(2x+1)=5?

Nov 7, 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:

$2 x + 1 = - 5$

$2 x + 1 - \textcolor{red}{1} = - 5 - \textcolor{red}{1}$

$2 x + 0 = - 6$

$2 x = - 6$

$\frac{2 x}{\textcolor{red}{2}} = - \frac{6}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = - 3$

$x = - 3$

Solution 2:

$2 x + 1 = 5$

$2 x + 1 - \textcolor{red}{1} = 5 - \textcolor{red}{1}$

$2 x + 0 = 4$

$2 x = 4$

$\frac{2 x}{\textcolor{red}{2}} = \frac{4}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = 2$

$x = 2$

The Solutions Are: $x = - 3$ and $x = 2$

Nov 7, 2017

$x = \left\{2 , - 3\right\}$

#### Explanation:

We can tackle this by considering how $| a | = | - a |$

So hence;

$| - \left(2 x + 1\right) | = | 2 x + 1 | = 5$

So hence, $2 x + 1 = 5$
But also $- \left(2 x + 1\right) = 5$

As $| - \left(2 x + 1\right) | = | 2 x + 1 |$

So hence solving both linear equations we yield;

$x = \left\{2 , - 3\right\}$