Solving Absolute Value Inequalities

[holmes1172]

So, I'm just going to walk through this and if somebody could tell me if I'm on the right track or not...

|7-3x|>4
7-3x<-4 or 7-3x>7

7-3x=-4
Now, can I take (-3x) and move it up front to say -3x+7 is less than -4 or do I have to leave it as 7-3x is less than -4?

 

[pka]

|7-3x|>4

\(\displaystyle |7-3x|=|3x-7|>4\). That is easier to solve.

Now solve the two: \(\displaystyle 3x-7>4~\&~3x-7<-4~.\)

 

[holmes1172]

\(\displaystyle |7-3x|=|3x-7|>4\). That is easier to solve.

Now solve the two: \(\displaystyle 3x-7>4~\&~3x-7<-4~.\)

|7-3x|>4
7-3x<-4 or 7-3x>4
-3x-7<-4 or -3x-7>4
-3x<-3 or -3x>-11
X<1 or x>3.2

Something is telling me I shouldn't have ended up with 3.2 though...lol. Could you let me know what I did wrong?

 

[Quaid]

|7 - 3x| > 4


7 - 3x < -4

or

7 - 3x > 7

You threads display several typographical errors, holmes. (People in this forum may begin skipping your posts, once they realize that much time is needed for deciphering your text.)

Please begin proofreading your posts before submission. Use the [Preview Post] button for that!

7 - 3x = -4

Why did you write an equation here? (Is that a typo, too?)

can I take (-3x) and move it up front to say

-3x + 7

or do I have to leave it as

7 - 3x

JeffM addressed this, in your other thread.

Did you read his reply about The Commutative Property of Addition? :???:

 

[holmes1172]

You threads display several typographical errors, holmes. (People in this forum may begin skipping your posts, once they realize that much time is needed for deciphering your text.)

Please begin proofreading your posts before submission. Use the [Preview Post] button for that!




Why did you write an equation here? (Is that a typo, too?)




JeffM addressed this, in your other thread.

Did you read his reply about The Commutative Property of Addition? :???:

No, you did. You're right. I guess I was just hoping maybe it didn't apply here. Sorry. I've gotten feedback about my typos and I will clean those up. Just getting used to the forum, for which I'm very appreciative! I'm taking an online math class and don't have much access for help, so you can guess how much I love this forum for helping me understand better.

Also, I see what you did there to get the 1. That makes a lot more sense and I can understand how to go about it now. Very nice. Little understanding on how really changes the solution.

 

[holmes1172]

Well, maybe I should ask. To get 1, did you subtract 3 from the -4?

 

[pka]

Well, maybe I should ask. To get 1, did you subtract 3 from the -4?

Look at reply #2.

\(\displaystyle \\3x-7>4\\3x>11\\x>\dfrac{11}{3}\)

\(\displaystyle \\3x-7<-4\\3x<3\\x<1\)

Thus the solution set is \(\displaystyle (-\infty,1)\cup\left(\dfrac{11}{3},\infty\right)\)

 

[Dale10101]

Suggestion

No, you did. You're right. I guess I was just hoping maybe it didn't apply here. Sorry. I've gotten feedback about my typos and I will clean those up. Just getting used to the forum, for which I'm very appreciative! I'm taking an online math class and don't have much access for help, so you can guess how much I love this forum for helping me understand better.

Also, I see what you did there to get the 1. That makes a lot more sense and I can understand how to go about it now. Very nice. Little understanding on how really changes the solution.

M. Holmes, you are a rascal. Your typos and misused math expression are making everyone chase you around the block, fatigue is inevitable.

This link tells how to write math symbols using the keyboard. http://www.purplemath.com/modules/mathtext.htm

Also, it appears (only offering my opinion) that you are missing steps in your math skills development. I think, and I may be wrong, that it was you who said that you are learning via an online course and were missing detailed examples worked out and a teacher to conference with. (I might be thinking of someone else.) At any rate it seems to me that your time would be most profitably spent working problems which are accompanied by detailed solutions so that you could learn a regular procedure for solving standard problems.

THIS very website freemathhelp.com offers detailed explanations and many examples of how to work standard problems.

Home page: http://www.freemathhelp.com/index.html
Algebra page: http://www.freemathhelp.com/algebra-help.html

I am in no way saying that you should not ask questions I am suggesting that you will learn more efficiently if you broaden your approach.

Below is a link that I am updating and offers several way of entering algebraic equations on a posting page. You should probably learn to use the keyboard method as referenced above but you might like to know about other options.

I admire your tenacity ... don't give up, yes ask for help but help us by expressing yourself more clearly. Thanks.

PS. If you email me I can give your the title of a humongous book of Algebra problems that is based on one example after another of detailed, no steps left out, solved algebra problems with helpful notes tacked in as bubbles. Use it myself. Is costs about $7 used and $11 - $17 new + shipping, through Amazon. Good luck.

 

[stapel]

...I can give your the title of a humongous book of Algebra problems that is based on one example after another of detailed, no steps left out, solved algebra problems with helpful notes tacked in as bubbles. Use it myself. Is costs about $7 used and $11 - $17 new + shipping, through Amazon.

Sounds interesting. Info, please?