rwangs
Answered

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how to find x(x-2)<0

Sagot :

salomerailoa

Answer:

x<2

Step-by-step explanation:

x- 2 <0

x < 2

theleangreenbean

Answer:

[tex]0<x<2[/tex]

Step-by-step explanation:

Hi there!

[tex]x(x-2)<0[/tex]

Set x(x-2) equal to 0:

[tex]x(x-2)=0[/tex]

Solve for x by using the zero product property:

[tex]x(x-2)=0[/tex]

[tex]x=0[/tex] and [tex]x=2[/tex]

Now, we know that for the inequality [tex]x(x-2)<0[/tex], one of the following must be true:

1) [tex]0<x<2[/tex]

2) [tex]x<0[/tex] or [tex]x>2[/tex]

To find out which one it is, 1) or 2), we can substitute a value into [tex]x(x-2)<0[/tex] to see if the inequality is true.

For example, 1 takes place in between 0 and 2. If 1 satisfies [tex]x(x-2)<0[/tex], then [tex]0<x<2[/tex] must be true. If it does not, then [tex]x<0[/tex] or [tex]x>2[/tex] must be true:

[tex]1(1-2)<0\\1(-1)<0\\-1<0[/tex]

This inequality is true. Thus, [tex]0<x<2[/tex].

I hope this helps!

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