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Chapter 5: Problem 1

On a number line indicate all numbers greater than or equal to \(-\frac{1}{2}\) but less than \(\frac{3}{4}\).

Short Answer

Expert verified
Question: Represent all numbers greater than or equal to -1/2 and less than 3/4 on a number line. Answer: To represent the given interval on the number line, draw a horizontal line and mark the points -1/2 and 3/4. Indicate that -1/2 is included in the interval with a solid circle or square bracket ([), and show that 3/4 is not included in the interval with an open circle or round bracket ( ). Then, draw a line segment between these two points, including the point at -1/2 and excluding the point at 3/4. This line segment represents all numbers greater than or equal to -1/2 but less than 3/4 on the number line.

Step by step solution

01

Draw a number line

First, draw a horizontal line. This line represents the number line, where each point on the line corresponds to a number, and the distance between points represents the difference between the numbers.
02

Mark the endpoints

On the number line, locate the points that correspond to \(-\frac{1}{2}\) and \(\frac{3}{4}\). These are the endpoints of the interval representing the numbers greater than or equal to \(-\frac{1}{2}\) and less than \(\frac{3}{4}\). To make these points more visible, draw a small vertical line segment at these points.
03

Indicate the interval

Now, we need to show the interval on the number line. Since the numbers in the interval are greater than or equal to \(-\frac{1}{2}\), draw a solid circle or square bracket ( [ ) at \(-\frac{1}{2}\) to indicate that this point is included in the interval. Then, since the numbers in the interval are less than \(\frac{3}{4}\), draw an open circle or round bracket ( ) at \(\frac{3}{4}\) to indicate that this point is not included in the interval.
04

Draw a line connecting the two points

To represent the numbers in the interval, draw a line segment between the points \(-\frac{1}{2}\) and \(\frac{3}{4}\) on the number line, including the point at \(-\frac{1}{2}\) and excluding the point at \(\frac{3}{4}\). This line segment represents all the numbers greater than or equal to \(-\frac{1}{2}\) but less than \(\frac{3}{4}\) on the number line. Now, the number line visually represents all numbers greater than or equal to \(-\frac{1}{2}\) but less than \(\frac{3}{4}\).

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