SOLUTION: abs |2x-1| + 1

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Question 178221This question is from textbook
: abs |2x-1| + 1 < 6 This question is from textbook

Found 2 solutions by Lj, jim_thompson5910:
Answer by Lj(2) (Show Source):
You can put this solution on YOUR website!
Basically, absolute value is always positive. It means how many the value is from zero.
To solve this equation, we isolate the variable.
|2x-1|<5
Then find the absolute value of -1, which is one. Then use opposite operations to isolate the variable completly.

Then divide by two.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Start with the given inequality

Subtract 1 from both sides.

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

Divide 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 on a number line, you would get

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

SOLUTION: abs |2x-1| + 1 < 6