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

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Answer 1 · 2016-04-15T21:01:50

$x>=7$

You have to divide the resolution into three parts:

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

$-x-(-x+7)=7$

$-x+x-7=7$

$0=14$

No solution

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

$x-(-x+7)=7$

$x+x-7=7$

$2x=14$

$x=7$ (solution)

3)if $x>=7$ : the equation turns into:

$x-(x-7)=7$

$x-x+7=7$

$0=0$ 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 $x>=7$ .

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