algebra math problem easy 10 points (:?

x^2 - 2x ≥ 15
x^2 - 2x - 15 ≥ 0
x^2 + 3x - 5x - 15 ≥ 0
(x^2 + 3x) - (5x + 15) ≥ 0
x(x + 3) - 5(x + 3) ≥ 0
(x + 3)(x - 5) ≥ 0

x + 3 ≤ 0
x ≤ -3

x - 5 ≥ 0
x ≥ 5

∴ x ≤ -3, x ≥ 5

x² - 2x ≥ 15
x² - x ≥ 15 + (- 1)²
x² - x ≥ 15 + 1
(x - 1)² ≥ 16
x - 1 ≥ ± 4

x ≥ 4 + 1, x ≥ 5
x ≥ - 4 + 1, x ≥ - 3

Answer: x ≥ 5, - 3 OR x ≥ 5 ≥ - 3

x^2 - 2x ≥ 15
x^2 - 2x -15 ≥ 0
(x + 3) (x - 5) ≥ 0

Now x^2 - 2x - 15 is a parabola pointing up with roots x = -3 and x = 5. Therefore, it will be > 0 to the left of smaller root (x < -3), and to the right of larger root (x > 5)

(x + 3) (x - 5) ≥ 0
x ≤ -3 or x ≥ 5

x^2 - 2x ≥ 15
x^2-2x-15≥ 0
(x+3)(x-5)≥ 0
At x-axis, when f(x)=0,
(x+3)(x-5) =0
x=-3 or x=5

If you do a sketch of the graph of this quadratic function, it is concave up and you will also notice that only any x-values less than 3 or greater than 5(i.e.,x<-3 or x>5) will result in the inequality greater than 0.

x^2 - 2x ≥ 15

x^2 - 2x - 15 ≥ 0

(x - 5)(x + 3) ≥ 0

x - 5 ≥ 0
x ≥ 5

x + 3 ≥ 0

x ≥ -3

Since x must be greater than 5, we can scrap the last solution.

ok, you have even have been given your self a share. you could resolve any share with the help of "flow multiplying." it will make greater experience in case you in case you positioned 10/a million=20/x. You multiply the right with the different backside. (the 1st numerator with the 2d denominator) 20=10x is what you get. then you definitely divide the two facets with the help of 10 to get: x=2

x ² - 2x - 15 ≥ 0

( x - 5 ) ( x + 3 ) ≥ 0

( x - 5 ) ≥ 0 and ( x + 3 ) ≥ 0
x ≥ 5 and x ≥ - 3------------------------>x ≥ 5

( x - 5 ) and ( x + 3 ) ≥ 0

( x - 5 ) ≤ 0 and ( x + 3 ) ≤ 0
x ≤ 5 , x ≤ - 3----------------------------> x ≤ - 3

Sol set = { x : x ≤ - 3 U x ≥ 5 , x Є R }

x^2 - 2x ≥ 15
x^ - 2x - 15 ≥ 0
(x-5)(x+3) ≥ 0

x ≥ 5, x ≥ -3

x^2 - 2x ≥ 15
x^2-2x-15>=0
x^2-5x+3x-15>=0
x(x-5)+3(x-5)>=0
(x+3)(x-5)>=0
x+3>=0 or x-5<=0
x>=-3 or x<=5
-3<=x<=5