1. inequality

I have a inequality

3 - x / 2 > 7

I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

My method;

First get rid of the denominator 2

3 - x > 2 x 7

Then move 3 to the RHS

x > 14 - 3

x > 11

Now if I put 11 in the inequality the answer is - 2.5

so the result; - 2.5 > 7 is wrong?

Is my method wrong or am I just to show how to get X on it's own?

Thanks

David

2. Re: inequality

x > 11

11 is not greater than 11 !

3. Re: inequality

Originally Posted by David Green
I have a inequality

(3 - x)/2 > 7

I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

My method;

First get rid of the denominator 2

3 - x > 2 x 7

Then move 3 to the RHS

- x > 14 - 3

- x > 11

x < -11
...

4. Re: inequality

Originally Posted by skeeter
...
I see it know, X I knew had to be on it's own, but I didn't think about changing the sides to get X on it's own?

-x > 11 here X is not alone

x < - 11 here X is alone

Thanks

David

5. Re: inequality

Originally Posted by David Green
I have a inequality

3 - x / 2 > 7

I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

My method;

First get rid of the denominator 2

3 - x > 2 x 7

Then move 3 to the RHS

x > 14 - 3

x > 11

Now if I put 11 in the inequality the answer is - 2.5

so the result; - 2.5 > 7 is wrong?

Is my method wrong or am I just to show how to get X on it's own?

Thanks

David
Obtain a positive x on one of the two sides, viz

$\displaystyle \frac{3-x}{2}>7$

Double both sides

$\displaystyle \frac{2(3-x)}{2}>2(7)$

$\displaystyle 3-x>14$

$\displaystyle 3-x+x>14+x$

$\displaystyle 3>x+14$

$\displaystyle x+14<3$

Subtract 14 from both sides

$\displaystyle x+14-14<3-14$

$\displaystyle x<-11$