How Do You Solve the Modulus Inequality x|x - 2| ≥ 1?

[nyrychvantel]

For $$x|x - 2| \ge 1$$,

since $$|x - 2| \ge 0$$, and for $$x|x - 2| \ge 1$$,
so $$x > 0$$

Since $$x > 0$$, can I multiply the x inside to make it $$|{x^2} - 2x| \ge 1$$ ??


Or can you teach me your method of solving this question?
Thanks.

 

[praharmitra]

modulus function questions are usually solved by taking cases.

x > 2 and x < 2

Take the value of the mod according to the two cases and solve it.. After you solve the inequality for one case, you will get a bound for x. Don't forget to put this together with x > 2 to get the actual bound for x...

Accordingly do the next one