Inequalities: If 3 less than 4 times a number is....

[nathan]

I am trying to help my son with this problem:

If 3 less than 4 times a number is greater than or equal to 3 less than 7 times the number, What is the largest the number can be?

I had difficulty helping him; I'm not sure if this is right, but this is what we got:

. . . 4x - 3 > 7x - 3

This is probably very simple, but I did not how to help him. Any hints will be appreciated. Thank you!

 

[arthur ohlsten]

I agree with
4x-3<=7x-3
add 3 to both sides
4x<=7x
subtract 4x from each side
0<=3x divide both sides by 3
0<=x

x is any positive number or 0

Arthur

 

[nathan]

Arthur

I want to thank you so much for your help---Now we understand and he less stress.

we did the same except we did not divide both side by 3--it makes sence---

 

[skeeter]

Re: HELP with inequalities --

If 3 less than 4 times a number is greater than or equal to 3 less than 7 times the number, What is the largest the number can be?

\(\displaystyle \L 4x - 3 \geq 7x - 3\)

\(\displaystyle \L 4x \geq 7x\)

\(\displaystyle \L 0 \geq 3x\)

\(\displaystyle \L 0 \geq x\) ... or \(\displaystyle \L x \leq 0\)

x is any non-positive number.