RashmiT wrote:

@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4

|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3

-2x+1 = -2x-3

1=-3

which is invalid???

RashmiT , you are correct.

My brain clearly was not working well.

Nice catch, +1, thank you, and my apologies.

With two absolute value terms in an equation, you can open mods.

With more than two mods?

If, as here, the answers are before you, use them.

If answers are not before you, use

"

Critical Method" see

chetan2u,

Absolute Modulus, A Better Understanding and

Bunuel , "

3-steps approach for complex problems,"

Absolute Value Modulus, 3-steps approach And "

Graphical Method,"

chetan2u ,

Absolute Modulus, A Better Understanding (You probably know what to do when there are more than two absolute value expressions. I post these links just in case you might need them, but mostly to help people who have not seen the excellent posts to which the links refer.)

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"