# How do you solve |x + 6| = 2x and find any extraneous solutions?

Jun 16, 2016

#### Answer:

$x = - 2$ if $x < - 6$
$x = 6$ if$x \ge - 6$

#### Explanation:

Knowing the property of absolute value that says:

if$| x | = a$ then
$x = - a , x < 0$

$x = a , x \ge 0$

Applying the above property we have:

$x + 6 = - 2 x , x + 6 < 0$. Eq(1)

$x + 6 = 2 x , x + 6 \ge 0$. Eq(2)

Solving the above equations we have:

Eq(1): if $x + 6 < 0$ that is $x < - 6$
$x + 2 x = - 6$
$3 x = - 6$
$x = - \frac{6}{3} = - 2$
So,
$x = - 2 , x < - 6$

Eq(2): if $x + 6 \ge 0$ that is $x \ge - 6$

$x + 6 = 2 x$
$x - 2 x = - 6$
$- x = - 6$
$x = 6$ whenever $x \ge - 6$