SOLUTION: |6-4x|>2

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

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

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
RELATED QUESTIONS
2x-2=4x+6 (answered by piglet162431)

6(2-x)=4x (answered by checkley71,MathLover1,jim_thompson5910)

6(2-x)=4x (answered by 13114,ganesh,jim_thompson5910)

4x^2+5x-6 (answered by jim_thompson5910)

x^2-4x=6 (answered by jsmallt9)

solve... (answered by stanbon)

4x^2 + 11x + 6 (answered by solver91311)

3x^2+4x+6 (answered by oberobic)