Find alternate solutions to absolute value functions

Question

For, the problem $|x + 1| = |2x - 1|$, I found one solution analytically:

$x + 1 = 2x - 1$

$\to x = 2$

Since, these are absolute functions, they should intersect once more at $x = 0$. This solution I got by guessing integers. Is it possible to find this solution analytically? My textbook says to graph the functions and find the other solution.

Answer 1

If two expressions have the same absolute value, then either they are equal or one is the negative of the other.

So either $x+1=2x-1$ or $x+1=-2x+1$.

So the two solutions are $x=2, x=0$.