Question Video: Graphing Linear Inequalities | Nagwa Question Video: Graphing Linear Inequalities | Nagwa

Question Video: Graphing Linear Inequalities Mathematics • Sixth Year of Primary School

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Which of the following diagrams represents the inequality −2 ⩽ 𝑥 < 1? [A] Diagram A [B] Diagram B [C] Diagram C [D] Diagram D

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Video Transcript

Which of the following diagrams represents the inequality 𝑥 is greater than or equal to negative two but less than one?

So, if we take a look at the inequality we have in this question, we can see that it’s a double inequality because we’ve got two inequality signs. And that is, it is an amalgamation of the two inequalities 𝑥 is greater than or equal to negative two and 𝑥 is less than one. And what this is gonna show is a region between two values. So, if we’re gonna want to represent this on a number line, what we need to do is remind ourselves of some of the notation we use.

So, if we take a look at the first inequality sign, we’ve got 𝑥 is greater than or equal to negative two. So, therefore, because it’s greater than or equal to, we’re gonna have a colored-in circle or dot in the line to the right because the colored-in circle or dot means or equal to rather than just that value. And then, the line to the right is gonna be greater than. Then, for the second part of our inequality, we’re gonna have an open circle. And that’s because it’s just 𝑥 is less than one. It’s not 𝑥 is less than or equal to one. And then we’re gonna have a line going off to the left because it’s less than. As we’d already said, this is a double inequality. So, it represent a region between two values. So, therefore, we’re gonna join the lines between our two dots or circles.

So, now, we’ve got something that looks like what we want. Well, we’re gonna represent our inequality on a number line. And we can also see that our colored circle is gonna be on the negative two. And the open circle is gonna be on the one. So, if we take a look at our possible answers, we can see that this is the same as answer (A). Because in answer (A), we have a colored-in circle on the negative two and an open circle on the one. So, what this shows is that 𝑥 can be any value between negative two and one which includes negative two, but doesn’t include one.

So, therefore, we can say that the diagram which represents the inequality 𝑥 is greater than or equal to negative two but less than one is diagram (A). And the other ones are incorrect for various reasons involving the number-line notation. So, (B) has the incorrect dot colored in and the incorrect dot open. In (C), they’re both colored in, and in (D), they’re both open, which will be all incorrect.

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