SOLUTION: What is the solution of the absolute value equation |3x-7|_<13

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Question 714840: What is the solution of the absolute value equation |3x-7|_<13
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
abs%283x-7%29%3C=13

If 3x-7%3E=0 --> abs%283x-7%29=3x-7 and the inequality is 3x-7%3C=13

If 3x-7%3C0 --> abs%283x-7%29=-%283x-7%29 and the inequality is -%283x-7%29%3C=13
Multiplying both sides tiles (-1) and reversing the "less than" sign, we get an equivalent inequality
-%283x-7%29%3C=13 --> 3x-7%3E=-13 <--> -12%3C=3x-7

Both cases can be written together as -12%3C=3x-7%3C=13
Adding 7 to all three sides of the compound inequality yields an equivalent inequality.
-12%3C=3x-7%3C=13 --> -12%2B7%3C=3x-7%2B7%3C=13%2B7 --> -6%3C=3x%3C=20
Dividing by 3 all three sides of the compound inequality yields an equivalent inequality that is the solution.
-6%3C=3x%3C=20 --> -6%2F3%3C=3x%2F3%3C=20%2F3 --> highlight%28-2%3C=x%3C=20%2F3%29