How do you solve and graph the solution set of |2x-1|<=2|2x−1|≤2?

1 Answer
Lil Del
Nov 8, 2016

The solution of the inequality is -0.5 <= x <= 1.5−0.5≤x≤1.5.

Explanation:

When solving an absolute value inequality, the process used actually depends upon which inequality symbol is in the original inequality. If the inequality symbol is << or <=≤, solve using an "and" compound inequality. If the inequality symbol is >> or >=≥, solve using an "or" compound inequality. Since this inequality has a <=≤ symbol, it will be solved using an "and" compound inequality.

|2x - 1| <= 2|2x−1|≤2

-2 <= 2x - 1 <= 2−2≤2x−1≤2

-2 + 1 <= 2x - 1 + 1 <= 2 + 1−2+1≤2x−1+1≤2+1

-1 <= 2x <= 3−1≤2x≤3

(-1)/2 <= (2x)/2 <= 3/2−12≤2x2≤32

-0.5 <= x <= 1.5−0.5≤x≤1.5

To graph this solution, put closed dots at -0.5−0.5 and 1.51.5 and shade the number line between the dots.

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