How do you solve $abs(x+3)=3x+1$ ?

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Answer 1 · 2016-09-06T19:45:25

The solution set is ${ 1}$ .

Case 1: The absolute value is positive

$x + 3 = 3x + 1$

$-2x = -2$

$x = 1$

Case 2: The absolute value is negative

$-(x + 3) = 3x + 1$

$-x - 3 = 3x + 1$

$-3 - 1 = 4x$

$-4 = 4x$

$x =-1$

However, checking, you will find $x = -1$ is extraneous.

Hence, the solution set is ${1}$ .

Hopefully this helps!

How do you solve abs(x+3)=3x+1abs(x+3)=3x+1?