Graph x≤−3 . Responses Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. A closed point is plotted at negative 3. An arrow extends indefinitely left from the closed point past negative 8 along the number line. Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. A closed point is plotted at negative 3. An arrow extends indefinitely right from the closed point past 2 along the number line. Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. An open point is plotted at negative 3. An arrow extends indefinitely right from the open point past 2 along the number line.

Question

Graph x≤−3 . Responses Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. A closed point is plotted at negative 3. An arrow extends indefinitely left from the closed point past negative 8 along the number line. Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. A closed point is plotted at negative 3. An arrow extends indefinitely right from the closed point past 2 along the number line. Image with alt text: A number line ranges from negative 8 to 2 in increments of 1. An open point is plotted at negative 3. An arrow extends indefinitely right from the open point past 2 along the number line.

Answer 1

The response is a description of three images. The first image shows a closed point plotted at -3 on a number line ranging from -8 to 2. There is also an arrow extending indefinitely left from the closed point beyond -8 on the number line.

The second image is similar to the first, but the arrow extends indefinitely right from the closed point beyond 2 on the number line.

The third image is similar to the second, but instead of a closed point, there is an open point plotted at -3.

Answer 2

To graph the inequality x ≤ -3 on a number line, follow these steps:

1. Draw a number line that ranges from a value less than -3 to a value greater than -3. In this case, the number line ranges from -8 to 2.

2. Plot a closed point (●) at -3.

3. Draw an arrow extending indefinitely to the left from the closed point (●), indicating that all values less than or equal to -3 should be shaded. The arrow should extend past -8.

The resulting graph should show a closed point (●) at -3, with an arrow extending indefinitely to the left, covering all values less than or equal to -3.

Answer 3

To graph the inequality x ≤ -3, we need to represent all the values of x that are less than or equal to -3 on a number line.

First, draw a horizontal number line that ranges from a number smaller than -3 (e.g., -8) to a number larger than -3 (e.g., 2). Make sure to include the numbers in between, separated by equally spaced intervals.

Next, plot a closed point (a solid dot) on the number line at -3. This represents the value of x being exactly -3, including it in the solution set.

Finally, since we want all the values less than -3, draw an arrow to the left of the closed point that extends indefinitely. This arrow represents all the values to the left of -3, including -8 or any number between -3 and -8.

The result should be a number line with a closed point at -3 and an arrow extending infinitely to the left.

An alternative way to represent the inequality is to plot an open point (an empty dot) at -3 instead of a closed point. Then, draw an arrow to the right of the open point that extends indefinitely. This indicates that the set of values includes any number greater than -3, but not -3 itself.

I have provided some images to help visualize these representations. Please note that the number line ranges from -8 to 2, with an interval of 1. The images show both the closed point and open point versions of the graph.