Question Video: Identifying the Linear Inequality Represented on a Given Number Line | Nagwa Question Video: Identifying the Linear Inequality Represented on a Given Number Line | Nagwa

Question Video: Identifying the Linear Inequality Represented on a Given Number Line Mathematics • Second Year of Preparatory School

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Which of the following diagrams represents the inequality −3 < 𝑥 ≤ 0? [A] Diagram A [B] Diagram B [C] Diagram C [D] Diagram D [E] Diagram E

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Video Transcript

Which of the following diagrams represents the inequality 𝑥 is greater than negative three and less than or equal to zero?

We know that when representing inequalities on a number line, an open circle represents greater than or less than. A closed or colored-in circle, on the other hand, represents greater than or equal to or less than or equal to. When the circle is colored in, we’re including that number.

In our inequality, 𝑥 is greater than negative three. This means that we need an open circle at negative three. 𝑥 is less than or equal to zero. This means that we need a closed circle at zero.

The correct answer is therefore option (A) as there is an open circle at negative three and a closed circle at zero.This shows the inequality 𝑥 is greater than negative three and less than or equal to zero.

Option (B) has the circles the wrong way round. This means that 𝑥 is greater than or equal to negative three and less than zero. In option (C), both of the circles are open. This means that 𝑥 is greater than negative three and less than zero. In option (D), both the circles are closed or colored in, so 𝑥 is greater or equal to negative three and less than or equal to zero. In option (E), we only have one circle. This is colored in at zero. 𝑥 could therefore take any value that is less than or equal to zero. All four of these options are incorrect.

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