SOLUTION: |6-4x|>2

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Question 177246: |6-4x|>2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%286-4x%29%3E2 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)

6-4x+%3C+-2 or 6-4x+%3E+2 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 6-4x+%3C+-2


6-4x%3C-2 Start with the given inequality


-4x%3C-2-6Subtract 6 from both sides


-4x%3C-8 Combine like terms on the right side


x%3E%28-8%29%2F%28-4%29 Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3E2 Divide


Now lets focus on the second inequality 6-4x+%3E+2


6-4x%3E2 Start with the given inequality


-4x%3E2-6Subtract 6 from both sides


-4x%3E-4 Combine like terms on the right side


x%3C%28-4%29%2F%28-4%29 Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3C1 Divide



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Answer:

So our answer is

x+%3C+1 or x+%3E+2


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