Question

Decide whether the ordered pair is a solution of the inequality. $$y>3 x^{2}+50 x+500 ;(-6,100)$$

Short answer

No, the ordered pair (-6,100) is not a solution of the inequality \(y > 3x^2 + 50x + 500\).

Step-by-step solution

Identification

Identify the ordered pair (-6,100) where the first value is x = -6 and the second value is y = 100.

Substitution

Substitute these values into the inequality: 100 > 3(-6)^2 + 50(-6) + 500.

Simplification

Simplify the right side of the inequality: 100 > 3*36 + (-300) + 500, which simplifies further to 100 > 108 - 300 + 500 and finally to 100 > 308.

Comparison

Compare the left side (100) to the right side (308) and determine if the inequality stands: As 100 is not greater than 308, the provided ordered pair (-6,100) is not a solution to the inequality.