Question

HELP PLEASE, BRAINLIEST IF CORRECTTT Rewrite each equation without absolute value for the given conditions: y=|x−3|+|x+2|−|x−5|, if x<-2

1. 1. y=|x−3|+|x+2|−|x−5|, if -2<x< 3  = x
2. y=|x−5|+|x+5|, if x>5 = 2x
3. y=|x−5|+|x+5|, if x<−5 = -2x
4. y=|x−5|+|x+5|, if −5<x<5 = 10
Modulus value means it always gives positive value. Therefore,
Step-by-step explanation:
if x < a, then |x – a| is positive when |x – a | = a -x, which is positive as a is larger than x.
and if x >a, then |x-a| is positive when |x-a| = x – a, which is positive as a is smaller than x.
Applying the same,
(1) for  -2 < x < 3,
|x – 3 | = 3 – x, as x <3
| x + 2 | = | x – (-2)| = x – (-2) = x+2 as x> -2
| x – 5 | = 5 -x , as x < 5
therefore, y = |x−3|+|x+2|−|x−5| = 3 – x + x + 2 – (5 – x) = x
(2) for x > 5,
|x – 5|= x – 5
|x  + 5| = | x – (-5)| = x + 5
therefore y = x – 5 + x + 5 = 2x
(3) for x < -5,
|x – 5| = 5 – x
|x + 5| = |x – (-5)| = -5-x
therefore y = 5 – x + -5 -x = -2x
(4) for -5< x < 5,
|x -5| = 5 – x
|x +5| = x + 5
y = 5 – x + x + 5 = 10