# How do you solve |-7x + 7| = 14?

Aug 4, 2016

$x = - 1$
$x = 3$

#### Explanation:

$- 7 x + 7 = 14$
or
$- 7 x = 14 - 7$
or
$- 7 x = 7$
or
$x = - \frac{7}{7}$
or
$x = - 1$................Ans$1$

Now consider
$- 7 x + 7 = - 14$
or
$- 7 x = - 14 - 7$
or
$- 7 x = - 21$
or
$7 x = 21$
or
$x = \frac{21}{7}$
or
$x = 3$.....................Ans$2$

Aug 4, 2016

$x = - 1 \text{ and "x=3" }$ are solutions

#### Explanation:

Remember that everything inside the two | | is read as positive. This is called an 'absolute' value

Written as in the question or as 'abs(-7x+7)=14'

$\textcolor{b r o w n}{\text{Observe where the red and blue lines cross. It is evident that this}}$ $\textcolor{b r o w n}{\text{expression gives two values for "x" as an answer.}}$

The part of the equation inside the | | may be positive or negative but will always be read as a final positive overall value.

Thus what is inside the | | has the possibility to be -14 or +14 and still satisfy the equation

Suppose $- 7 x + 7 = 14$

$\textcolor{b l u e}{\text{Then "-7x=7" " =>" } x = \left(- 1\right)}$

Suppose $- 7 x + 7 = - 14$

$\textcolor{b l u e}{\text{Then "-7x=-21" "=>" } x = 3}$