I don't know how to properly type up all the mathematical symbols on here so this might look a bit stupid...

-4>x-4

3x-4 1

But yeah, I can solve this up to where I get

-4>3x^2-16x+16

And now what do I do with it??

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- Nov 21st 2010, 01:24 PMMathSucks123Solving Rational Inequalities
I don't know how to properly type up all the mathematical symbols on here so this might look a bit stupid...

__-4____>____x-4__

3x-4 1

But yeah, I can solve this up to where I get

-4__>__3x^2-16x+16

And now what do I do with it?? - Nov 21st 2010, 01:47 PMdwsmith
Add 4 to both sides and then factor the quadratic. After that, put the values that solve the quadratic on a number line and see which ranges make the equation true.

Also, it maybe more in your favor to have a better name than MathSucks123 when wanting help from people who think the contrary. - Nov 21st 2010, 03:54 PMwilly0625
First of all we have to assume, cannot be since if it was, it makes the L.H.S. of the orginial inequality undefined.

Multiplying both sides by , (and since we are sure this is greater than 0), we obtain

which gives

strong inequaltiy since or

You can actually consider different cases like Soroban did below, but it's up to you which approach you employ. - Nov 21st 2010, 03:57 PMSoroban
Hello, MathSucks123!

Quote:

Do NOT multiply through by an expression containing

. . unless you take responsibility for what happens

. . when that expression happens to be negative.

Solve the**equation**: .

We get: .

. .

Note that the first fraction is undefined when

These divide the number line into four intervals.

. .

Test a value in each interval and see if it satisfies the inequality.

. . . Yes

. . . no

. . . Yes

. . no

The solution is: .