SOLUTION: the was is inequality of /x-4/>3

Algebra ->  Absolute-value -> SOLUTION: the was is inequality of /x-4/>3      Log On


   

Question 174988: the was is inequality of /x-4/>3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-4%29%3E3 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)

x-4+%3C+-3 or x-4+%3E+3 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality x-4+%3C+-3


x-4%3C-3 Start with the given inequality


x%3C-3%2B4Add 4 to both sides


x%3C1 Combine like terms on the right side


Now lets focus on the second inequality x-4+%3E+3


x-4%3E3 Start with the given inequality


x%3E3%2B4Add 4 to both sides


x%3E7 Combine like terms on the right side



----------------------------------------------------

Answer:

So our answer is

x+%3C+1 or x+%3E+7


which looks like this in interval notation





if you wanted to graph the solution set on a number line, you would get

Graph of the solution set in blue and the excluded values represented by open circles