# How do you solve abs(4x+1)=11?

Mar 29, 2018

$x = \frac{5}{2} \setminus , x = - 3$

#### Explanation:

$| 4 x + 1 | = 11$
$4 x + 1 = 11 \setminus , 4 x + 1 = - 11$ (Definition of $| a |$)
$4 x = 11 - 1 \setminus , 4 x = - 11 - 1$
$4 x = 10 \setminus , 4 x = - 12$
$x = \frac{10}{4} \setminus , x = - \frac{12}{4}$
$x = \frac{5}{2} \setminus , x = - 3$

Mar 29, 2018

$x = - 3 \text{ or } x = \frac{5}{2}$

#### Explanation:

$\text{the expression inside the bars of the absolute value can}$
$\text{be positive or negative}$

$\textcolor{b l u e}{\text{Positive value}}$

$4 x + 1 = 11$

$\Rightarrow 4 x = 11 - 1 = 10$

$\Rightarrow x = \frac{10}{4} = \frac{5}{2}$

$\textcolor{b l u e}{\text{Negative value}}$

$- \left(4 x + 1\right) = 11$

$\Rightarrow - 4 x - 1 = = 11$

$\Rightarrow - 4 x = 11 + 1 = 12$

$\Rightarrow x = \frac{12}{- 4} = - 3$

$\textcolor{m a \ge n t a}{\text{As a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$| \left(4 \times \frac{5}{2}\right) + 1 | = | 11 | = 11 = \text{ right side}$

$| \left(4 \times - 3\right) + 1 | = | - 11 | = 11 = \text{ right side}$

$\Rightarrow x = - 3 \text{ or "x=5/2" are the solutions}$

Mar 29, 2018

$x = 2.5$

#### Explanation:

The lines are just saying absolute value which is the distance from zero. So all you have to do is get rid of those...
$4 x + 1 = 11$
subtract 1 from both sides and get... $4 x = 10$
then, divide 4 on both sides and you get $x = 2.5$