There's an equation that we got assigned to solve in our first college math class. I was alright at math in high school, but I've never seen an absolute value equation similar to this one.
|||||x|+x|+x|+x|+x| = 2018
I'm guessing we have to split it in 2 cases, one in which
+x >= 0
and
-x < 0
How should I approach this problem?
If $x \geq 0$, then $2x, 3x, 4x, 5x$ are also non-negative, and the LHS is $$ |||||x|+x|+x|+x|+x| = ||||2x|+x|+x|+x| = \dotsb = 5x,$$ so $5x = 2018 \implies x = 2018/5$.
If instead $x < 0$, then $|x| = -x$, and the LHS is $$ |||||x|+x|+x|+x|+x| = ||||-x+x|+x|+x|+x| = ||||0|+x|+x|+x| = |||x|+x|+x| = ||-x+x|+x| = |0+x| = |x| = -x,$$ so $-x = 2018 \implies x = -2018$.