Solve for x.
-ax + 3b > 5
x > the quantity 3 times b minus 5 all over negative a
x > the quantity 5 minus 3 times b all over negative a
x < the quantity 3 times b plus 5 all over negative a
x < the quantity negative 3 times b plus 5 all over negative a

- anonymous

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- anonymous

@nincompoop

- dan815

okay so if you were to subtract the same quantitity from both sides the inequality still holds

- dan815

for example|
say
we have
5>4
which is true
if we subtract 2 from both sides
5-2>4-2
we just shifted the numbers down by 2
3>2

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## More answers

- dan815

same thing with multiplication

- dan815

suppose
a > b
then
3a>3b is still true

- dan815

|dw:1435216228375:dw|

- anonymous

subtract 3 from each side?

- anonymous

nvm

- dan815

the final rule you need to know is

- dan815

multiplication by -1 or any negative number, here is where the inequality flips

- dan815

if
a > b
then
-a < -b

- dan815

this can be seen more clearly with number line examples

- dan815

|dw:1435216365389:dw|

- dan815

|dw:1435216407582:dw|

- dan815

the distance from the 0 is the same, however now a is MORE negative and b is LESS negative

- dan815

so -a<-b
and a>b

- dan815

ill leave you with an excercise show this is still true, when a is negative and b is positive to start with

- dan815

lool

- dan815

that guy called us nerds and left

- dan815

arent u enraged

- Astrophysics

lol

- Astrophysics

slow down dan

- anonymous

im just so confused

- Astrophysics

thats what dan does he throws bunch of info at you and expects you to get it, he's a noobie, im the hero I'll save you

- Astrophysics

lolol

- dan815

make sure u read all that over! after astros help

- dan815

its important, please do it

- anonymous

you lost me at "if
a > b
then
-a < -b"

- dan815

imagine the number line,

- anonymous

yeah that number line got me confused lol

- Astrophysics

I think you should do the algebra first and then you can figure it out

- Astrophysics

Dan gave lots of good info, but he's a hyper one and a smart one :P, so lets take it down a bit.

- anonymous

please lol

- Astrophysics

|dw:1435216787284:dw| so this is what we're given right and we need to solve for x, so a rule I'll say right now, when we do algebra with inequalities, if we multiply OR divide by a negative number the sign of the inequality flips ok?

- anonymous

ok

- Astrophysics

Great, so lets start off and do our algebra, any idea what we can do with 3b?

- anonymous

divide it with 3?

- Astrophysics

Well, we want to move everything but the x on the left side, meaning we isolate x/ solving x. So to do this an easy way to look at it is, do the opposite of what operation already exists, so notice we have +3b to cancel it out (we want 0 3b's on the left) we would subtract it, as follow: |dw:1435217000808:dw| and remember what we do to one side we MUST also do it to the other.

- Astrophysics

That should say to the right side sorry* :P

- Astrophysics

|dw:1435217056160:dw| so now we have this, let me know when you're ready to move on

- anonymous

ok got it

- Astrophysics

Alright cool, so what should we do next, remember we want to keep x there, but not the -a, but we can't have -a be 0 otherwise x will be 0 to and it would make no sense!

- Astrophysics

What operation do you think would be best :)

- anonymous

get rid of the -a by adding a?

- Astrophysics

Nice try, but notice it's "attached" to the x, that means it's being multiplied, so we divide by -a on both sides!

- Astrophysics

Also remember the little rule I mentioned earlier, what happens if we divide by a negative sign?

- anonymous

it becomes a positive?

- Astrophysics

I mean to the inequality

- Astrophysics

|dw:1435217372626:dw| remember the sign flips

- anonymous

oh yeah my bad

- Astrophysics

|dw:1435217417366:dw| now we can put it in words, I will let you figure that out!

- Astrophysics

But everything so far makes sense right?

- anonymous

so far yes

- Astrophysics

Ok so try comparing it with one of your options and see if you can get it

- Astrophysics

Or you can leave the answer as |dw:1435217588112:dw|

- anonymous

option A?

- Astrophysics

Mhm, is it x< or is it x>

- Astrophysics

You be able to eliminate two answers right away

- anonymous

>

- Astrophysics

Lol just look at the answer

- Astrophysics

It's right there!

- anonymous

it doesnt show the same answer for the options

- Astrophysics

|dw:1435217852979:dw|

- anonymous

doesnt show the same answer

- anonymous

3b+5/a?

- Astrophysics

\(\color{blue}{\text{Originally Posted by}}\) @CatalystDuzIt
Solve for x.
-ax + 3b > 5
x > the quantity 3 times b minus 5 all over negative a
x > the quantity 5 minus 3 times b all over negative a
x < the quantity 3 times b plus 5 all over negative a
x < the quantity negative 3 times b plus 5 all over negative a
\(\color{blue}{\text{End of Quote}}\)
We can eliminate the first one and the second option, so look at three and four.

- Astrophysics

I think this will make it clear |dw:1435217982712:dw|

- Astrophysics

|dw:1435218006866:dw|

- anonymous

yeah thats it

- anonymous

thanks man. i appreciate it!

- Astrophysics

No worries, the answers they gave you are in a way you would never put...so yeah haha.

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