Compare the graph of a compound inequality involving and with the graph of a compound inequality involving or.

more than -5 and less than +5

-5 < x < +5
line between x = -5 and +5

less than -5 or more than +5
-5 > x > +5
line left of -5, skip -5 to + 5 and line right of +5

Eh? I've never seen an or written like that... It's always been in two parts:

x < -5 OR x > +5

When comparing the graphs of compound inequalities involving "and" and "or," it's important to understand how each operator affects the solution set.

1. Compound Inequality with "and" (Intersection):
A compound inequality involving "and" represents the intersection of two separate inequalities. To graph this compound inequality, you need to locate the solution sets of both individual inequalities and find their overlap.

For example, let's consider the compound inequality -1 ≤ x < 3 and 2 ≤ x ≤ 5:

First, graph the inequality -1 ≤ x < 3:
- Draw a solid dot at -1 (inclusive) on the number line.
- Draw an open dot at 3 (exclusive) on the number line.
- Shade the line segment between -1 and 3.

Next, graph the inequality 2 ≤ x ≤ 5:
- Draw a solid dot at 2 (inclusive) on the number line.
- Draw a solid dot at 5 (inclusive) on the number line.
- Shade the line segment between 2 and 5.

Finally, determine the overlap of the two shaded regions. This overlap represents the solution set for the compound inequality.

2. Compound Inequality with "or" (Union):
A compound inequality involving "or" represents the union of two separate inequalities. To graph this compound inequality, you need to combine the solution sets of both individual inequalities.

Continuing with the previous example, let's consider the compound inequality -1 ≤ x < 3 or 2 ≤ x ≤ 5:

First, graph the inequality -1 ≤ x < 3 (same as before).

Next, graph the inequality 2 ≤ x ≤ 5 (same as before).

Finally, combine both shaded regions into one larger shaded region. This combined region represents the solution set for the compound inequality involving "or."

In summary, a compound inequality involving "and" represents the overlap (intersection) of two inequalities, while a compound inequality involving "or" represents the combination (union) of two inequalities.

To compare the graphs of compound inequalities involving "and" and "or," we need to understand the meanings of these operators.

In mathematics, the operator "and" represents the intersection of two sets, while the operator "or" represents the union of two sets.

Let's start by understanding compound inequalities involving "and." Suppose we have the compound inequality:

a < x < b and c < x < d

To graph this compound inequality, we need to graph each individual inequality and then find the overlapping region. Here are the steps to do that:

1. Graph the first inequality: a < x < b
- Draw a number line.
- Mark point a and point b.
- Use an open circle to represent the points a and b if the inequality is strict, or a closed circle if it is inclusive.
- Shade the region between a and b because it represents the values that satisfy the inequality.

2. Graph the second inequality: c < x < d
- Draw a number line.
- Mark point c and point d.
- Use an open circle to represent the points c and d if the inequality is strict, or a closed circle if it is inclusive.
- Shade the region between c and d because it represents the values that satisfy the inequality.

3. Find the overlapping region:
- Identify the common shaded region between the two inequalities.
- This common region represents the values that satisfy both inequalities, i.e., the compound inequality a < x < b and c < x < d.

Now let's move on to compound inequalities involving "or." Suppose we have the compound inequality:

a < x < b or c < x < d

To graph this compound inequality, we need to graph each individual inequality and then combine the shaded regions. Here are the steps to do that:

1. Graph the first inequality: a < x < b
- Follow the same steps as explained earlier to graph the inequality a < x < b.

2. Graph the second inequality: c < x < d
- Follow the same steps as explained earlier to graph the inequality c < x < d.

3. Combine the shaded regions:
- Shade the regions between a and b as well as between c and d.
- The combined shaded region represents the values that satisfy either the inequality a < x < b or c < x < d.

To summarize, when comparing the graph of a compound inequality involving "and" with a compound inequality involving "or":

- The graph of the compound inequality involving "and" shows the overlapping region of the individual inequalities.
- The graph of the compound inequality involving "or" shows the combined region of the individual inequalities.

Remember, the process of graphing inequalities is essential for understanding and analyzing their solutions visually.