Need Help Solving Division Inequality

[roadman]

I'm a parent who hasn't had algebra problems in over 30 years. My wife, an Accountant, is out of town on business, so, I'm trying to help my 8th grade daughter.

Here is the problem:

X< 2x-15
_____
3

I've tried to rack my brain on how to solve this, but I just can't recall how to solve these problems.

I don't even know where to begin.

Thank you in advance if someone can show the process.

 

[Denis]

X< 2x-15
_____
3

Is the 3 under he X? Like X / 3 < 2x - 15 ?
Or is it X < (2x - 15) / 3

/ is division sign.

Also: should the X be x ?

 

[roadman]

Sorry about that, now I know my algebra skills have diminished.

Question #1.

The 3 is under the 2x-15.

Question #2.

The first "x" should be x.

Thank you.

 

[arthur ohlsten]

x<2x-15 add 15 to each side
15+x<2x subtract x from each side
15<x

OR IS IT
X/3 < 2X-15 MULTIPLY BOTH SIDES BY 3
x<6x-45 add 45 to each side
x+45<6x subtract x from each side
45<5x
9<x

OR IS IT
x<[2x-15]/3 multiply both sides by 3
3x<2x-15 subtract 2x from each side
x<-15

Arthur

 

[Denis]

OK; so we have x < (2x - 15) / 3

Step 1: multiply each side by 3 to get rid of fraction:
3x < 2x - 15

Step 2: Subtract 2x from each side so the x's are isolated:
3x - 2x < 2x - 2x - 15
x < -15 : that means x is lesser than -15, like -16, -17 ....

That's it...over and out :wink:

 

[roadman]

Thank you both so much.

My daughter went to bed frustrated, but we will hit it early in the am.

Thank you again.

 

[arthur ohlsten]

you are welcome

Please tell your daughter to handle <,and > signs the same as = signs.
With one major difference, multiplying with a - sign [or dividing] change the sign.

example:
x<4 subtract x and 4 from each side
-4<-x now multiply by -1
4<x WRONG WE MUST REVERSE THE < SIGN TO >

THE BEST ADVISE IS TO TRY TO NOT MULTIPLY ,OR DIVIDE , BY A MINUS SIGN
Arthur