SOLUTION: draw the number line graph which is the solution of |x-2| less than 5

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Question 118430: draw the number line graph which is the solution of |x-2| less than 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28x-2%29%3C5 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3C+a, then x+%3E+-a and x+%3C+a)

x-2+%3E+-5 and x-2+%3C+5 Break up the absolute value inequality using the given rule


-5+%3C+x-2+%3C+5 Combine the two inequalities to get a compound inequality



-3+%3C+x+%3C+7 Add 2 to all sides


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Answer:

So our answer is

-3+%3C+x+%3C+7



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