How do you solve the equation $absx=x+3$ ?

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Answer 1 · 2017-05-09T19:12:55

Use the definition:

$|x|= {(x;x >=0),(-x;x < 0):}$

Given: $absx=x+3$

Use the definition to break into two equations:

$x = x+3; x >=0$ and $-x = x+3; x < 0$

Subtract x from both sides of both equations:

$0 = 3; x >=0$ and $-2x = 3; x < 0$

Discard the first equation, because it can never be true:

$-2x = 3; x < 0$

Divide both sides by -2 and drop the restriction because it will obviously be true:

$x = -3/2$

Check:

$|-3/2| = -3/2+3$

$3/2=3/2$

This checks

$x = -3/2 larr$ answer.

How do you solve the equation absx=x+3absx=x+3?