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Write the solution set of each inequality if x is an element of the set of integers.$x^{2}-4 x+4>0$

$\{x | x<2 \text { or } x>2\},\{\ldots, 0,1,3,4, \ldots\}$

Algebra

Chapter 1

THE INTEGERS

Section 8

Quadratic Inequalities

The Integers

Equations and Inequalities

Polynomials

Missouri State University

Baylor University

Lectures

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In mathematics, the absolu…

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Write the solution set of …

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Solve each inequality. Wri…

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and this question. We want to write the solution, set up each inequality if X is an element in the centre manager. So here we have extreme minus four rifles for greater than zero. So first, let's factor this factor. Extra miles four. It was four. We know that the constant four. We're gonna look at it and find the multiples that will equal for so that sounded kind of convoluted. But what I mean is what numbers will most likely get? Four. We have four and 12 and two. And so what combination to have to use, we're gonna have to use fact that negative two squares four so that we have X minus two squared is how we factor this. Because then we would have X squared minus two x minus two X, which gives us minus four X and then minus two times minus two, is positive for no one to say. This is great in zero. So let's find that factor, which is X equals two. That's where we have zero and we use a little number line. So put two right there. So let's pick a value above two and see what we get If we pick something like three and plug it in, we get a positive number. So that works. And if we pick something below to, like a negative number negative three, we plugged it in. That also works. And the easiest way to know this is because if something is square, it's always me positive. So basically four X that is any numbers we could say ex lesson to X ray than two, except for X equals to, because that would give us zero. And that is not what the inequalities asking for all these real numbers of suffer, too, will satisfy this inequality.

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