Need help solving the inequality

[jazzgirl]

9/x-4 >7/x-4

Not sure what to do. Do I set it to 0?

 

[Deleted member 4993]

9/x-4 >7/x-4

Not sure what to do. Do I set it to 0?

Is this:

$\displaystyle \frac{9}{x} - 4 > \frac{7}{x} - 4$

or

$\displaystyle \frac{9}{x - 4} > \frac{7}{x - 4}$

 

[garf]

Hi Jazzgirl!
Remember that in inequalities the > or < changes when you divide or multiply by a negative number:
3*2<4*2
multiplying by -1:
-6>-8
So, you have to consider cases and suppose that your denominator (either x-4 or x) is positive or negative and isolate x following the same rules than equations, but also considering the sign.
Let me know if this helps,
GARF

 

[soroban]

Hello, jazzgirl!

$\displaystyle \text{Solve for }x\!:\;\;\frac{9}{x-4} \:>\:\frac{7}{x-4}$

We can take reciprocals if we reverse the inequality.

. . . . . . . . . . . . .$\displaystyle \frac{x-4}{9} \;<\;\frac{x-4}{7}$

$\displaystyle \text{Multily by 63:} \;\;\:7(x-4) \;<\;9(x-4)$

. - - . . . . . . .. $\displaystyle 7x - 28 \;<\;9x-36$

. . . . . . . . . . . . . $\displaystyle -2x \;<\;-8$

. . $\displaystyle \text{Divide by }-2\!:\quad\;\; x \;>\;4$

 

[jazzgirl]

It is the latter.

I am not sure what you are saying. My denominator is X-4 on both. So where do I start?

 

[jazzgirl]

soroban,
Thanks. This will help me with my others.
Jazzgirl

 

[mmm4444bot]

I am not sure what you are saying.

We are saying that your original typing is ambiguous; there was no way for us to determine for sure what the denominators were, until you clarified.

You can avoid ambiguity, in the future, by always typing grouping symbols around numerators or denominators that are algebraic expressions.

Here is the proper way to type your original inequality, using a keyboard:

9/(x - 4) > 7/(x - 4)

Without the parentheses, typing "9/x - 4" means that the number -4 is being added to the fraction 9/x.

"See" the difference?

Click HERE to see examples of how to type math, using a keyboard.

 

[jazzgirl]

Got it thanks.