need clarification with inequalities (1 Viewer)

[kangarulz]

with the inequalities with results like: (x-2)(x+1)>0 or (x-1)(x+3)(x-2)<0, etc how do you when to reverse the sign? and also does it make a difference to the result if the question asks (2-x) instead of (x-2) (where the x and the number has switched positions)

 

[B35tY]

I'm not too sure what you're asking, but i'll try to help.

To solve the inequality (x-2)(x+1)>0

Firstly, it should be apparent that the equation (x-2)(x+1)>0 has roots at x = 2 and x = -1

Then, by expanding the first terms of each bracket (getting x^2), you can see that the graph will be a normal parabola (as opposed to an upside down parabola, which would be the case if the coefficient of x^2 was negative).

Then, draw a quick graph and it's easy to see that the answer is x > 2 or x < -1

Of course, if you had (2 - x) instead of (x - 2) then the coefficient of x^2 would be -1 and then the answer would be -1<x<2 instead..

Did i help?

 

[ThuanSUX]

I agree with b35ty about drawing the parabola. From the factorized form you can mark your roots on the x-axis. From here draw it out (remember to watch out for the (2-x) case because the parabola is heading downwards).

If you want f(x) < 0, then it's the part of the parabola under the x-axis
If you want F(x) > 0, then it's the upper part.

There is a large difference between (x-2) and a (2-x) factor. Although the roots are the same, the curve is up-side-down. This means your answers to the inequality should have the opposite signs.

Eg: (x-2)(x+3) > 0
Ans: x<-3 and x>2

Eg: (2-x)(x+3) > 0
Ans: -3 < x < 2

 

[Riviet]

If you want f(x) < 0, then it's the part of the parabola under the x-axis
If you want F(x) > 0, then it's the upper part.

This isn't true for all continuous functions.
Instead, you could think of it like this:
Say you have some function f(x)>0. Sketch the graph as stated by others with the x-intercepts and any important info that might be useful. Ask yourself, "for what values of x is the curve above the x-axis?" Determine these x-values and that will give your solution.

In general,

For f(x)>0, determine the x-values for which f(x) is strictly above the x-axis.

For f(x)>0, determine the x-values for which f(x) touches OR is above the x-axis.

For f(x)<0, determine the x-values for which f(x) is strictly below the x-axis.

for f(x)<0, determine the x-values for which f(x) touches OR is below the x-axis.

 

[ThuanSUX]

In general,

For f(x)>0, determine the x-values for which f(x) is strictly above the x-axis.

For f(x)>0, determine the x-values for which f(x) touches OR is above the x-axis.

For f(x)<0, determine the x-values for which f(x) is strictly below the x-axis.

for f(x)<0, determine the x-values for which f(x) touches OR is below the x-axis.

That's what I meant, but I couldn't figure out how to do the greater/equal and lesser/equal symbol and cbf looking.

This isn't true for all continuous functions.

I believe what I said was correct. For f(x) > 0, you simply use the > sign instead of >, and likewise for lesser than.