Question

If |x-3|+2|x+1|=4, then value of x lies in the interval
a) x € (0,4)
b) x € (2,5)
c) x € (-3,0)
d) x € (-5,-1)​

Answer 1

Answer:

Let’s first state a few conditions

Case 1: x+1≤0→x≤−1

So opening the modulus function,

−(x−3)−2(x+1)=4

→−x+3−2x−2=4

→−3x=3→x=−1

This is there in the domain set by the condition, so x = -1 is one solution

Case 2: x+1>0;x−3≤0

→ −1<x≤3

-(x-3) + 2(x+1) = 4

→ x = -1

But this term is not specified in the current domain (besides we already obtained the same value)

Case 3: x−3>0 → x>3

(x−3)+2(x+1)=4

→ x=53<3

This value too doesn’t satisfy the domain set for this condition.

So the only value we obtain is x=−1

Hope it helps.