Math problem?

Question

i know the answer to this problem, but i dont know how to get there:
l2yl=l3y+2l+1
the answer should be y={-1,-3/5}

Answer 1

case1: y< -2/3
-2y= -3y-2 +1
y= -1
case2: -2/3<=y< 0
-2y=3y+2+1
-5y=3
y= -3/5
case 3: y>=0
2y=3y+2+1
-y=3
y= -3
but case 3 does not satisfy the given eq. therefore ans. are case1 & case2

Answer 2

In handling equations with absolute value it's fundamental to know the definition of absolute value:

| argument| = argument if argument=>0
| argument| = negative of argument if argument < 0

That is how SS astutely made her 3 cases. Note that in her 3rd case the "solution" contradicts her assumption that y >= 0. Therefore the "solution" is nullified.

Sometimes it might prove helpful to draw a graph of the sign behavior of each argument, so you can see at a glance what the absolute value quantity will convert to, in the region you're investigating.

(2y) ----------|-------0+++++++++
(3y+2) --(-2|3)+++++++++++++