Find all values (inequality) of r that guarantee r - 2|x-2| = 8 has no solutions for x?

Question

(A) {r | r < 8}

(B) {r | r >= 10}

(C) {r | r <= 2}

(D) {r | r > -4}

Answer 1

r - 2 l x - 2 l = 8

l x - 2 l = (r-8) / 2

l x - 2 l is never negative

So, the equation above has no solution if (r - 8) / 2 < 0

r - 8 < 0

r < 8