Question

Розв’язати рівняння: |x+3| - |x-5|=3x+4

Answer 1

Ответ: x = - 4

Объяснение:

$|x + 3| - |x-5| = 3x + 4 \\\\ x + 3= 0 ~~ ; ~~ x -5 = 0 \\\\ x = -3~~~ ~~ ; ~~ x =5$

$\underline{ | ~~~\pmb{\sf l}~~~ | ~~~ \pmb{\sf l l }~~~| ~~~ \pmb{\sf lll } ~~~ | ~~~~}_ > {_x} \\ ~~~~~ -3 ~~~ ~ ~~~ 5 \\ ~~~\pmb-~~ ~~ ~~ \pmb +~~ ~~ ~~ \pmb+ ~~~~~~~~~~~~~ x +3 \\ ~~~\pmb-~~ ~~ ~~ \pmb -~~ ~~ ~~ \pmb+ ~~~~~~~~~~~~~ x-5$

$\hspace{-2em} I) ~~ -(x+3) - (-(x-5) ) = 3x + 4 \\\\ -x-3 + x - 5 = 3x + 4 \\\\ 3x + 4 = -8 \\\\ x= - 4 ~~ \checkmark ~~ ; ~~ x \in (-\infty ~ ; ~ -3 )$


$\hspace{-2em} II) ~~ (x+3) - (-(x-5) ) = 3x + 4 \\\\ x+3 + x - 5 = 3x + 4 \\\\ 2x -2 = 3x + 4 \\\\ x= - 6 ~~ \varnothing ~~ ; ~~ x \in ( -3 ~ ; ~ 5 )$

$\hspace{-3em} III) ~~ (x+3) -(x-5) = 3x + 4 \\\\ x+3 - x +5 = 3x + 4 \\\\ 3x + 4 = 8 \\\\ x= 4/3 ~~ \varnothing ~~ ; ~~ x \in (~ 5 ~~ ; ~~ \infty ~ )$