solve 2x-x^2>0
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2x - x^2 > 0
x(2 - x) > 0
x > 0 and 2 - x > 0 OR x < 0 and 2 - x < 0
x > 0 and x < 2 OR x < 0 and x > 2
x < 0 and x > 2 has no solution so discard it, leaving just
x > 0 and x < 2
0 < x < 2
x(2 - x) > 0
x > 0 and 2 - x > 0 OR x < 0 and 2 - x < 0
x > 0 and x < 2 OR x < 0 and x > 2
x < 0 and x > 2 has no solution so discard it, leaving just
x > 0 and x < 2
0 < x < 2
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solve 2x-x^2>0
-x^2 + 2x > 0..........Multiply by " - 1 "......remember to change inequality sign
x^2 - 2x < 0............Factor
x(x - 2) < 0
Critical points are......x=0...and...x-2=0
Critical points are.....x=0.........x=2
Theses critical points seperate the number line into THREE section:
.........LEFT of 0...........between 0 and 2..............RIGHT of 2
................................0.....…
<-------------------------I-----------…
These three sections have either a NEGATIVE or POSITIVE sign associated with them. To find that
their sign pick a number from the region, substitute into X(X-2) and do you get a "+" or "-" answer.
That is the sign of that region.
................................0.....…
<-------------------------I-----------…
Select...-3.........................Se…
(-3)(-3-2)............................…
(-)(-)="+"region..............(+)(-)="…
................................0.....…
<-------------------------I-----------…
.................+....................…
Do you shade the "+" regions or the"-" region
Look at the inequality sign..................<0............numb… < 0 are Negative
......................................… the Negative region.
Solid Circles or Brackets.......OR........Open Cirlces or Parenthesis
Solid if their is an "="............................Open if their is not an "="
<......we will use an Open Circle on the 0 and on the 2 and shade BETWEEN them
Put this answer
ANSWER.......0 < x < 2..................OR.......( 0 , 2 )
If you have questions on this or any other math problem feel free
to let me know how to contact you.......Read Below.......
I tutor free online since moving to France from Florida in June 2011.
Hope this is most helpful and you will continue to allow me to tutor you.
If you dont fully understand or have a question PLEASE let me know
how to contact you so you can then contact me directly with any math questions.
If you need me for future tutoring I am not allowed to give out my
info but what you tell me on ***how to contact you*** is up to you
Been a pleasure to serve you Please call again
Robert Jones.............f
"Teacher/Tutor of Fine Students"
-x^2 + 2x > 0..........Multiply by " - 1 "......remember to change inequality sign
x^2 - 2x < 0............Factor
x(x - 2) < 0
Critical points are......x=0...and...x-2=0
Critical points are.....x=0.........x=2
Theses critical points seperate the number line into THREE section:
.........LEFT of 0...........between 0 and 2..............RIGHT of 2
................................0.....…
<-------------------------I-----------…
These three sections have either a NEGATIVE or POSITIVE sign associated with them. To find that
their sign pick a number from the region, substitute into X(X-2) and do you get a "+" or "-" answer.
That is the sign of that region.
................................0.....…
<-------------------------I-----------…
Select...-3.........................Se…
(-3)(-3-2)............................…
(-)(-)="+"region..............(+)(-)="…
................................0.....…
<-------------------------I-----------…
.................+....................…
Do you shade the "+" regions or the"-" region
Look at the inequality sign..................<0............numb… < 0 are Negative
......................................… the Negative region.
Solid Circles or Brackets.......OR........Open Cirlces or Parenthesis
Solid if their is an "="............................Open if their is not an "="
<......we will use an Open Circle on the 0 and on the 2 and shade BETWEEN them
Put this answer
ANSWER.......0 < x < 2..................OR.......( 0 , 2 )
If you have questions on this or any other math problem feel free
to let me know how to contact you.......Read Below.......
I tutor free online since moving to France from Florida in June 2011.
Hope this is most helpful and you will continue to allow me to tutor you.
If you dont fully understand or have a question PLEASE let me know
how to contact you so you can then contact me directly with any math questions.
If you need me for future tutoring I am not allowed to give out my
info but what you tell me on ***how to contact you*** is up to you
Been a pleasure to serve you Please call again
Robert Jones.............f
"Teacher/Tutor of Fine Students"
-
(x^2 -2x)<0
add 1 both side
(x^2 -2x +1)<1
(x-1)^2 < 1
Taking sqrt
x-1 < 1 or x-1<-1
x<2 or x< 0 .................Ans
add 1 both side
(x^2 -2x +1)<1
(x-1)^2 < 1
Taking sqrt
x-1 < 1 or x-1<-1
x<2 or x< 0 .................Ans