SOLUTION: Solve the following inequalities and write your answer in interval notation. |x-2| less than or equal to 7

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Question 1052352: Solve the following inequalities and write your answer in interval notation.
|x-2| less than or equal to 7
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-2%29%3C=7


TWO CONDITIONS:
x-2 is non-negative;
x-2 is negative.
Solve for both conditions.


x-2%3E=0
-
x-2%3C=7
x%3C=7%2B2
x%3C=9


x-2%3C0
-
abs%28x-2%29%3C=7
-%28x-2%29%3C=7
-x%2B2%3C=7
-x%2B2-7%3C=0, just doing this way to avoid multiplying by negative value;
-x-5%3C=0
-5%3C=x


Both conditions to be true
highlight%28-5%3C=x%3C=9%29

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