# Thread: Need a website to confirm inequalities with modulus operations

1. ## Need a website to confirm inequalities with modulus operations

I've been avoiding this but I need to really get the hang of it.
Teacher wont explain shit.

If you know a website or software that displays steps and solution on solving inequalities with modulus, I'd appreciate, rep and thank you.

2. I'm assuming you are talking about an algebra problem like: 4|2x-1|-2=10 ? Could you give an example?

Anyway, these are the websites that I use:

Symbolab (Recommended)
Free and shows all the steps plus "rules" if applicable. For example if you are solving trig problems it gives you the trigonometric identities for solving within the steps.

Mathway
Free but doesn't show the steps to solving unless you buy a subscription. I say its a bit more user friendly than Symbolab but thats just me. I mainly use this for quick checking of my answers and Symbolab for complete walkthroughs.

One of my favorites. It has a load of videos on many different school topics and its math section is like having a computer "tutor" helping you learn how to do the operations. Its totally free, and is good for students, parents, and teachers alike. I highly recommend looking into it if you teacher isn't explaining well enough, just start at the Math section, find your grade, and then your topic.

Hope this helps. Now back to my own math problems :P

3. ## The Following User Says Thank You to Necc For This Useful Post:

Mokou-Sama (09-26-2014)

4. Originally Posted by Necc
I'm assuming you are talking about an algebra problem like: 4|2x-1|-2=10 ? Could you give an example?

Anyway, these are the websites that I use:

Symbolab (Recommended)
Free and shows all the steps plus "rules" if applicable. For example if you are solving trig problems it gives you the trigonometric identities for solving within the steps.

Mathway
Free but doesn't show the steps to solving unless you buy a subscription. I say its a bit more user friendly than Symbolab but thats just me. I mainly use this for quick checking of my answers and Symbolab for complete walkthroughs.

One of my favorites. It has a load of videos on many different school topics and its math section is like having a computer "tutor" helping you learn how to do the operations. Its totally free, and is good for students, parents, and teachers alike. I highly recommend looking into it if you teacher isn't explaining well enough, just start at the Math section, find your grade, and then your topic.

Hope this helps. Now back to my own math problems :P
Yeah I know, I use symbolabs.
Thing is: I want to know how to solve step by step this one.

2<|x-1|=<3

If possible, or just this once, post the resolution of this one, i'd apreciate.
Because I want to know how to solve them, since I never knew and always managed to pass withouth knowing these. Now I cant go further.

5. Originally Posted by gamer4evere

Yeah I know, I use symbolabs.
Thing is: I want to know how to solve step by step this one.

2<|x-1|=<3

If possible, or just this once, post the resolution of this one, i'd apreciate.
Because I want to know how to solve them, since I never knew and always managed to pass withouth knowing these. Now I cant go further.
Sorry for taking so long to reply, been busy.

I'm guessing (only guessing!) that since it basically must be >2 and <3 then it wants interval notation: (2,3)

I would solve it like this:

2<|x-1|=<3 (Isolate the variable)

|x-1|=3 (Solve)

x-1=3 or x-1=-3 (Because we know that the absolute value of "x" = ±x, ie |1|=±1)

For x-1=3 (Add one to both sides)
x=4

For x-1=-3 (Add one to both sides)
x=-2
Easy and simple...

But oh wait! Back to the original equation, since |x-1| = -2 or 4 we have two answers, but since the original equation told us that 2<|x-1|=<3 (when the absolute value of x minus one is greater than two it equals greater than three) we know our answers can't be -2 or 4 because they aren't numbers between 2 and 3 so...idk. I'm only in Calculus so I may be missing something but I have never seen a problem like this. Are you sure that is the exact problem?

6. ## The Following User Says Thank You to Necc For This Useful Post:

Mokou-Sama (09-26-2014)

7. OK k no problema i got them already, will post correcta solution when i get home. THX anyway

8. Originally Posted by Necc
But oh wait! Back to the original equation, since |x-1| = -2 or 4 we have two answers, but since the original equation told us that 2<|x-1|=<3 (when the absolute value of x minus one is greater than two it equals greater than three) we know our answers can't be -2 or 4 because they aren't numbers between 2 and 3 so...idk. I'm only in Calculus so I may be missing something but I have never seen a problem like this. Are you sure that is the exact problem?
You're on the right track but you need to remember the comparison operators. So x >= -2 AND x <= 4 (alternatively -2 <= x <= -4) which satisfies the right side.

2 < | x-1 | <= 3

Remember the rules of inequalities:
x < (x is less than) means you also account for the negative value, swap sign, and some other stuff
x > (x is greater than) means you also account for the negative value, swap sign, and some other stuff

x-1 <= 3, x-1 >= -3
x-1 >= 2, x-1 <= -2

then
x <= 4, x-1 >= -2 (essentially -2 <= x <= 4, there are numbers that satisfy this and can use AND or write it like how i did)
x > 3, x < -1 (you can't combine these because there is no real number that is <-1 and also greater than 3 thus we need to use OR )

I'm not sure if there's any logic to this but you just find a relationship between your values. If you graph it you should see it. Lets just order these.
x >= -2
x < -1
x > 3
x <= 4

If we plug in -2, -1.01, 3.01, or 4, it satisfies both sides so we do not eliminate any of them.

We can combine the first two and the second two. You can be a number >= -2 but < -1 so I use AND. You cannot be a number
< -1 but also be > 3 thus these are two segmented regions so we use OR. You can be > 3 but <= 4 thus we use AND.

(x >= -2 AND x < -1) OR (x > 3 AND x <= 4)
Re-arrange them more:
-2 <= x < -1
OR
3 < x <= 4

Its easiest to see on the number line which I cannot graph. haha. If you graph it, its super easy to visual and you absolutely know whether or not you need to use OR or AND. Plus, sometimes after getting your possible results, one region might be completely obsolete or whatnot so it might not even be in the answer.

I dunno, wonder what the more standard way of doing it is? Anyway, lol... I'm so rusty in math. I remembered that you need to do something to remove the absolute value but forgot the rules so I looked it up. Anyway, GOOGLE to the rescue, too bad you can't use it on exams haha.

9. Wolframalpha .com solves about everything and gives you the opportunity to see the solution steps!

10. Wolfram alpha is the best but u need to have a premium account to see step to step

- - - Updated - - -

I would recommend that you search up the question on wolfram alpha and use the answer to work backwards until you get how to do it

11. i think you'll be able to get your hands on a cracked version of wolfram alpha on android quite easily, gives u step by step working too since the website doesn't unless you get premium access

12. I took all my math classes through math way. Worlds easiest app. Download it now. Math way.