How do I use a sign chart to solve x^2>4x2>4?

1 Answer
Jun 30, 2015

x^2 > 4x2>4 when x < -2x<2 and when x > 2x>2.

Explanation:

Let's modify the inequality by subtracting 44 from each side. Then

x^2 – 4 > 0

We start by finding the critical numbers.

Set f(x) = x^2 – 4 = 0 and solve for x.

(x+2)(x - 2) = 0

x+2 = 0 or x-2 = 0

x = -2 or x = +2

The critical numbers are -2 and +2.

Now we check for positive and negative regions.

We have three regions to consider: (a) x < -2; (b) -2< x <2; and (c) x >2.

Case (a): Let x = -3.

Then f(-3) = (-3)^2 - 4 = 9-4 = 5

f(x) > 0 when x < -2.

Case (b): Let x = 0.

Then f(0) = 0^2 -4 = 0-4 = -4

f(x) < 0 when -2 < x < 2

Case (c): Let x = 3.

Then f(3) = 3^2 - 4 = 9-4 = 5

f(x) > 0 when x > 2.

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If x^2 -4 > 0 when x < -2 and when x > 2,

x^2 >4 when x < -2 and when x > 2.