solving inequalities

[WlND]

Hi,

when does the sign change when solving inequalities again?
I think its when you divide by a negative for example

-2x<3
x> -(3/2)

but is there any other time?

Thanks

 

[tkhunny]

My favorite answer is "NEVER"!!

-2x < 3

Add 2x to both sides

0 < 3 + 2x

Subtract 3 from both sides

-3 < 2x

Divide both sides by "+2"

-3/2 < x

You never have to worry about switching inequalities again.

Really, do a little exploaration.

Is 2 < 5? Yes!

What happens if you multiply by +3

6 < 15 Still true? Yes. Can we conclude that multiplication by positive numbers is not a problem? Yes.

What happens if you Multiply by -3

-6 < -15 Still true? No. Better turn it around!

 

[WlND]

Thanks tkhunny!

 

[lookagain]

Hi,

when does the sign change when solving inequalities again?
At the moment/step you are dividing or multiplying
by a negative number/expression



I think its when you divide by a negative for example

-2x<3
x> -(3/2)

but is there any other time?
See above. Multiplication also is when it happens when it is
by a negative number.

Thanks

\(\displaystyle -2x \ < \ 3\)

\(\displaystyle \dfrac{-2x}{-2} \ > \ \dfrac{3}{-2}\)

\(\displaystyle x \ > \ \dfrac{-3}{2}\)


- - - - - - - - - - - - OR - - - - - - - - - - - - -


\(\displaystyle -2x \ < \ 3\)

\(\displaystyle \bigg(\dfrac{-1}{2}\bigg)(-2x) \ > \ \bigg(\dfrac{-1}{2}\bigg)(3)\)

\(\displaystyle x \ > \ -3/2\)


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


Here's another example:


\(\displaystyle -x \ \ge \ -5\)

\(\displaystyle \dfrac{-x}{-1} \ \le\ \dfrac{-5}{-1}\)

\(\displaystyle x \ \le \ 5\)


-------------------- OR ------------------------


\(\displaystyle -x \ \ge \ -5\)

\(\displaystyle (-1)(-x) \ \le \ (-1)(-5)\)

\(\displaystyle x \ \le \ 5\)



It is possible that certain fraction bars are not visible.

 

[WlND]

thanks for your reply lookagain!