Absolute Value Inequalities

Exercise 2.

Find the solutions of the inequality

\begin{displaymath}\vert 2x\vert\geq 6.\end{displaymath}


Let us first divide by 2:

\begin{displaymath}\vert x\vert\geq 3.\end{displaymath}

Thus we want to find all real numbers x whose distance to zero is at least 3. We are talking about the numbers in the interval $(-\infty,-3]$ and in the interval $[3,\infty)$.

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