# How do you solve for x:  −2|x − 3| = −12?

Jan 25, 2017

$\text{The Soln. Set=} \left\{- 3 , 9\right\} .$

#### Explanation:

$- 2 | x - 3 | = - 12$

$\therefore | x - 3 | = - \frac{12}{-} 2 = 6$

Removing $| \ldots | \text{ sign,}$ we have to consider $2 \text{ cases :}$"

$\text{Case } 1 : \left(x - 3\right) > 0 , i . e . , x > 3.$

In this Case, $\because \left(x - 3\right) > 0 , | x - 3 | = x - 3 , \text{ by Defn.}$

$\therefore x - 3 = 6 \Rightarrow x = 6 + 3 = 9 , \text{ & this } x > 3.$

$\text{Case } 2 : \left(x - 3\right) < 0 , i . e . , x < 3.$

$\therefore \text{ by Defn., } | x - 3 | = - \left(x - 3\right) = 3 - x .$

$\therefore | x - 3 | = 6 \Rightarrow 3 - x = 6 \Rightarrow x = 3 - 6 = - 3 , < 3.$

The Roots $x = - 3 , 9$ satisfy the given eqn.

$\text{Hence, the Soln. Set=} \left\{- 3 , 9\right\} .$

Enjoy the Maths.!