SOLUTION: Graphing absolute value inequalities. Could I have a step-by-step and reason why, PLEASE? Abs. (2b - 5) > 8 Thanks.

Algebra ->  Absolute-value -> SOLUTION: Graphing absolute value inequalities. Could I have a step-by-step and reason why, PLEASE? Abs. (2b - 5) > 8 Thanks.      Log On


   

Question 113266This question is from textbook Holt Algebra 1
: Graphing absolute value inequalities. Could I have a step-by-step and reason why, PLEASE?
Abs. (2b - 5) > 8
Thanks. This question is from textbook Holt Algebra 1

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

abs%282b-5%29%3E8 Start with the given inequality


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

2b-5+%3C+-8 or 2b-5+%3E+8 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 2b-5+%3C+-8


2b-5%3C-8 Start with the given inequality


2b%3C-8%2B5Add 5 to both sides


2b%3C-3 Combine like terms on the right side


b%3C%28-3%29%2F%282%29 Divide both sides by 2 to isolate b



b%3C-3%2F2 Reduce


Now lets focus on the second inequality 2b-5+%3E+8


2b-5%3E8 Start with the given inequality


2b%3E8%2B5Add 5 to both sides


2b%3E13 Combine like terms on the right side


b%3E%2813%29%2F%282%29 Divide both sides by 2 to isolate b



b%3E13%2F2 Reduce



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Answer:

So our answer is

b+%3C+-3%2F2 or b+%3E+13%2F2


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