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

Sep 6, 2016

The solution set is $\left\{1\right\}$.

Explanation:

Case 1: The absolute value is positive

$x + 3 = 3 x + 1$

$- 2 x = - 2$

$x = 1$

Case 2: The absolute value is negative

$- \left(x + 3\right) = 3 x + 1$

$- x - 3 = 3 x + 1$

$- 3 - 1 = 4 x$

$- 4 = 4 x$

$x = - 1$

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

Hence, the solution set is $\left\{1\right\}$.

Hopefully this helps!