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

Apr 15, 2016

$x \ge 7$

#### Explanation:

You have to divide the resolution into three parts:

1)if x<=0: the equation turns into:

$- x - \left(- x + 7\right) = 7$

$- x + x - 7 = 7$

$0 = 14$

No solution

2) if $0 < x \le 7$ : the equation turns into:

$x - \left(- x + 7\right) = 7$

$x + x - 7 = 7$

$2 x = 14$

$x = 7$ (solution)

3)if $x \ge 7$: the equation turns into:

$x - \left(x - 7\right) = 7$

$x - x + 7 = 7$

$0 = 0$ Universal solution (all values are possible, but remember we limited this part to x>=7)

Joining all the solution of the three branches we obtain solution as $x \ge 7$.