Question

|x-1| + |x-2| >= 4
please solve this...!!!

Answer 1

Answer:

your answer

Step-by-step explanation:

x−1|=(x−1) if x≥1 and |x−1|=−(x−1) if x<1

Also

|x−2|=(x−2) if x≥2 and |x−2|=−(x−2) if x<2

So:

If x≤1: |x−1|+|x−2|=−(x−1)−(x−2)=−2x+3

if x>1 and x<2: |x−1|+|x−2|=(x−1)−(x−2)=1

if x≥2:|x−1|+|x−2|=(x−1)+(x−2)=2x−3

So you want −2x+3≥4 for x≤1 and also 2x−3≥4 for x≥2.

So the answer is x≤−12 and x≥72.

So  x∈(−∞,−12]U[72,∞)