Question

Solving an inequality. x^2 >= x. How to choose right domain set of solutions, please, from the equations provided.

Answer 1

divide both sides by x then will get
x>= 1

Answer 2

x will be greater than two values in this case.

Answer 3

so you have
\[x^2 \ge x\]
\[x^2 - x \ge 0\]
\[x ( x -1 ) \ge 0\]

From this the book concludes that:
\[x \ge 1\] or
\[0 \ge x\]

Answer 4

I am not sure how it derives the solution set.
Does it follow like this?
\[(x - 1) \ge 0\]
\[x \ge 0\]
?
I am not sure how they get the solution
\[0 \ge x\]

Answer 5

yes for x<=0 this is right to

Answer 6

this is right too

Answer 7

How do you prove that mathematically from the equations?

Answer 8

-1^2 >= -1 true

yes ?

Answer 9

for zero are equale both sides

Answer 10

for -2^2 >= -2
4 > -2

Answer 11

ok ?