SOLUTION: the absolute value of 1/2x

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Question 119825: the absolute value of 1/2x - 1 < 1
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Start with the given inequality

Break up the absolute value (remember, if you have , then and )

and Break up the absolute value inequality using the given rule

Combine the two inequalities to get a compound inequality

Add 1 to all sides

Multiply all sides by 2 to isolate x

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Answer:

So our answer is

which looks like this in interval notation

if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the excluded values represented by open circles

SOLUTION: the absolute value of 1/2x - 1 < 1