Question

Determine solution set of the inequality

\[|x-1|\geq 3|x+1|\]

Answer 1

Interesting :)
We can always bring the 3 inside the absolute value...
\[\Large |x-1 |\ge |3x + 3|\]

Answer 2

Or... wait... rethinking...

Answer 3

Might be better to divide both sides by |x+1| instead
\[\Large \left|\frac{x-1}{x+1}\right|\ge 3\]

Answer 4

hmm

Answer 5

So that this means either
\[\Large \frac{x-1}{x+1}\ge 3\]or
\[\Large \frac{x-1}{x+1}\le -3\]

Answer 6

the solution is -2<x<-1/2 but i don't know how we got it ..

Answer 7

Patience. Solve this one:
\[\Large \frac{x-1}{x+1}\ge 3\]

Answer 8

ok..