Question

PLEASE HELP ME!! WILL GIVE BRAINLIEST :((

Rewrite without absolute value for the given conditions:
y=|x-3|+|x+2|-|x-5|, if 3

Answer 1

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Modulus value means it always gives positive value.

Therefore,

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

• Hope it will helps ✅