Question

Decide whether the ordered pair is a solution of the inequality. $$y \geq 2 x^{2}-8 x+8 ;(3,-2)$$

Short answer

Given ordered pair (3,-2) is not a solution to the inequality \(y \geq 2 x^{2}-8 x+8\).

Step-by-step solution

Understand the problem

An ordered pair consists of two values, namely \(x\) and \(y\). The task is to check if the ordered pair \((3, -2)\), when substituted into the inequality \(y \geq 2 x^{2}-8 x+8\), satisfies it.

Substitute the values

The value of \(x\) in the ordered pair is 3 and the corresponding value for \(y\) is -2. Substitute these values into the inequality. This leads to the following: -2 \(\geq 2(3)^2 - 8\times 3 + 8\).

Simplify the equation

Simplify the right hand side of the equation to get the numerical value. This should look like: -2 \(\geq 2\times 9 - 24 + 8\). Continued simplification leads to: -2 \(\geq 18 - 24 + 8 = 2\).

Check the validity of the inequality

Now, the inequality to be checked is -2 \(\geq 2\). This is false since -2 is not greater or equal to 2.