SOLUTION: |6-4x|>2

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

Start with the given inequality

Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule

Now lets focus on the first inequality

Start with the given inequality

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Divide

Now lets focus on the second inequality

Start with the given inequality

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Divide

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Answer:

So our answer is

or

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