Question

58.b on a number line, plot all possible values of x. -2 < x < 1.3 answer: tools: segment ray eraser your action: please select tool. number line from -3 to 3 with ticks at -3, -2, -1, 0, 1, 2, 3

Explanation:

Step1: Understand the inequality

The inequality is \(-2 < x < 1.3\), which means \(x\) is greater than \(-2\) and less than \(1.3\). So we need to represent the interval \((-2, 1.3)\) on the number line.

Step2: Select the appropriate tool

Since the interval is between two numbers (not including the endpoints), we use the "Segment" tool. We will place the start of the segment just to the right of \(-2\) (to indicate \(x > - 2\)) and the end of the segment just to the left of \(1.3\) (to indicate \(x < 1.3\)).

Step3: Plot the segment

On the given number line, find the position of \(-2\) (between \(-3\) and \(-1\), closer to \(-3\) but not including \(-2\)) and the position of \(1.3\) (between \(1\) and \(2\), \(0.3\) units to the right of \(1\) and not including \(1.3\)). Then draw a segment connecting the open circle (or the appropriate mark to show non - inclusion) just right of \(-2\) to the open circle just left of \(1.3\).

Answer:

To plot \( - 2

1. Use the "Segment" tool.
2. Mark the starting point just to the right of \(-2\) (to show \(x>-2\), an open circle conceptually at \(-2\) but the segment starts right after) and the ending point just to the left of \(1.3\) (to show \(x < 1.3\), an open circle conceptually at \(1.3\) but the segment ends right before).
3. Draw the segment between these two points on the number line.