# (Int. Algebra) I need help with an inequality problem

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• Sep 3rd 2018, 01:28 PM
alexcordero
(Int. Algebra) I need help with an inequality problem
Hello All,

So here's the problem. I got it right but I'm still not clear on flipping the sign. As I understand it, you flip the sign when you multiply or divide by a negative number. In the operation below, why is the sign "not" flipped (from -1/3)? That's the only I got wrong and admittedly, I still don't understand it.

Attachment 38912

Thanks.

ALex
• Sep 3rd 2018, 01:36 PM
romsek
Re: (Int. Algebra) I need help with an inequality problem
it's not flipped because you divide by 3, not negative 3.
• Sep 3rd 2018, 02:28 PM
alexcordero
Re: (Int. Algebra) I need help with an inequality problem
Ok... I understand your answer. I'm still a little confused because I thought that -1/3, 1/-3, and -(1/3) were all the same. Oh I think I see now... The entire inequality is divided by "3." The 3 doesn't suddenly change to "-3." The way I have it written makes it look like there are individual fractions. Right? Or am I still not getting it. Wow! you have to be really careful.
• Sep 3rd 2018, 02:47 PM
DenisB
Re: (Int. Algebra) I need help with an inequality problem
Solve (3x + 1)/4 = 2, then solve then solve (3x + 1)/4 = -3 : get my drift?
• Sep 3rd 2018, 02:53 PM
romsek
Re: (Int. Algebra) I need help with an inequality problem
Quote:

Originally Posted by alexcordero
Ok... I understand your answer. I'm still a little confused because I thought that -1/3, 1/-3, and -(1/3) were all the same. Oh I think I see now... The entire inequality is divided by "3." The 3 doesn't suddenly change to "-3." The way I have it written makes it look like there are individual fractions. Right? Or am I still not getting it. Wow! you have to be really careful.

let's just work through it

$-3 \leq \dfrac{3x +1}{4} \leq 3$

we first multiply everything by 4. inequality signs do not flip

$-12 \leq 3x+1 \leq 12$

we now subtract 1 from all sides.

$-13 \leq 3x \leq 11$

we now divide by 3, inequality signs do not flip

$-\dfrac{13}{3} \leq x \leq \dfrac{11}{3}$
• Sep 3rd 2018, 07:37 PM
alexcordero
Re: (Int. Algebra) I need help with an inequality problem
Quote:

Originally Posted by romsek
let's just work through it

$-3 \leq \dfrac{3x +1}{4} \leq 3$

we first multiply everything by 4. inequality signs do not flip

$-12 \leq 3x+1 \leq 12$

we now subtract 1 from all sides.

$-13 \leq 3x \leq 11$

we now divide by 3, inequality signs do not flip

$-\dfrac{13}{3} \leq x \leq \dfrac{11}{3}$

Ok, thank you very much for the explanation. On another question: How did you get the inequality and fractions to display as such?

Again, thanks for help.
• Sep 3rd 2018, 07:50 PM
Plato
Re: (Int. Algebra) I need help with an inequality problem
Quote:

Originally Posted by alexcordero
Ok, thank you very much for the explanation. On another question: How did you get the inequality and fractions to display as such?

If you click the tab reply with quote you will see the LaTeX code.

Here is some: -3 \leq \dfrac{3x +1}{4} \leq 3
-12 \leq 3x+1 \leq 12

You can warp the code \$-12 \leq 3x+1 \leq 12\$ in dollar signs you get $-12 \leq 3x+1 \leq 12$
• Sep 3rd 2018, 09:24 PM
alexcordero
Re: (Int. Algebra) I need help with an inequality problem
Quote:

Originally Posted by Plato
If you click the tab reply with quote you will see the LaTeX code.

Nice!! I'm going to find a LaTeX syntax cheat sheet. Thanks again.