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

1 Answer
Lil Del
Nov 8, 2016

The solution of the inequality is #-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#

#-2 <= 2x - 1 <= 2#

#-2 + 1 <= 2x - 1 + 1 <= 2 + 1#

#-1 <= 2x <= 3#

#(-1)/2 <= (2x)/2 <= 3/2#

#-0.5 <= x <= 1.5#

To graph this solution, put closed dots at #-0.5# and #1.5# and shade the number line between the dots.

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