SOLUTION: Find the value of x in the inequality ]x-7[ is less than or equal to 2. NOTE- ][ are absolute value signs. Thanks, Pat

Algebra ->  Inequalities -> SOLUTION: Find the value of x in the inequality ]x-7[ is less than or equal to 2. NOTE- ][ are absolute value signs. Thanks, Pat      Log On


   

Question 150515: Find the value of x in the inequality ]x-7[ is less than or equal to 2.
NOTE- ][ are absolute value signs.
Thanks,
Pat
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-7%29%3C=2 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-7+%3E=+-2 and x-7+%3C=+2 Break up the absolute value inequality using the given rule


-2+%3C=+x-7+%3C=+2 Combine the two inequalities to get a compound inequality



5+%3C=+x+%3C=+9 Add 7 to all sides


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Answer:

So our answer is

5+%3C=+x+%3C=+9



So the answer in interval notation is []


Also, the answer in set-builder notation is


Here's the graph of the solution set

Graph of the solution set

Note:
There is a closed circle at x=5 which means that we're including this value in the solution set
Also, there is a closed circle at x=9 which means that we're including this value in the solution set.