How to graph an absolute value inequality?

[gilmore3212003]

My question is to show interval notation and graph the following:

abs(4x-8)>12

What I got was x>5, the notation is (5, positive infinity), and there is a hole in the graph at x=5. I couldn't figure out how to draw the graph.

Please show me the graph. Also, can you tell me how to enter it into a TI89 calculator so that the graph will display?

 

[wjm11]

My question is to show interval notation and graph the following:

abs(4x-8)>12

What I got was x>5, the notation is (5, positive infinity), and there is a hole in the graph at x=5. I couldn't figure out how to draw the graph.

Hello, Gilmore,

You’ve only solved half the problem. When evaluating absolute value problems, one must set up two different equations/inequalities and solve both. The one you omitted is

4x-8 < -12 (Note that 12 became –12 and > switched to <)

which results in

x < -1

Therefore, the entire solution is

(-infinity,-1) OR (5, +infinity)

Since we are dealing with just one variable, x, in this problem, the graph is just a number line with open circles at both –1 and 5 and regions to the left and right of these values are shaded.

PS This is not a calculus problem. Please post problems in the correct forums.

 

[gilmore3212003]

This was a question from last nights quiz in my Calc. I class. I knew I hadn't done all the work. Thank you for solving this problem for me. By the way, where should I have posted this question (what subject/category)? The semester just started, so maybe it is a review.

 

[wjm11]

Yes, undoubtedly it's just review -- probably belongs in algebra.