2x≥3x+6≥6x-6
please explainn your answer, i dont know how to do it thanks
Split into two inequalities: $\displaystyle 2x \ge 3x+6$ and $\displaystyle 3x+6 \ge 6x-6$ and solve each one.
If $\displaystyle 2x \ge 3x+6$, solving for x we get $\displaystyle x \le -6$.
For the second inequality, $\displaystyle 3x+6 \ge 6x-6$, subtract 3x from both sides to get $\displaystyle 6 \ge 3x-6$. Add 6 to both sides to get $\displaystyle 12 \ge 3x \Rightarrow x \le 4$.
The solution set is the intersection of the sets defined by $\displaystyle x \le -6$ and $\displaystyle x \le 4$ (because x needs to satisfy both inequalities). This inequality follows the transitive property, so we do not need to worry about the inequality $\displaystyle 2x \ge 6x-6$. The solution set is $\displaystyle x \le -6$.