Understanding Compound Inequalities

This video tutorial introduces compound inequalities, explaining how to read and graph them. It covers open and closed intervals, using parentheses and square brackets, and provides examples to illustrate these concepts. The video also demonstrates how to write compound inequalities from word problems, ensuring a comprehensive understanding of the topic.

What is a compound inequality?

• A combination of two inequalities

• A graph with two lines

• An equation with two variables

• An inequality with a single variable

How do you graph an inequality that does not include its endpoints?

• Using square brackets

• Using dashed lines

• Using open points or rounded parentheses

• Using closed points

In interval notation, how is an open interval represented?

• With square brackets

• With curly braces

• With rounded parentheses

• With angle brackets

Which of the following is true for the inequality x > -1 and x < 2?

• x is between -1 and 2, excluding -1 and 2

• x is greater than 2

• x includes -1 and 2

• x is less than -1

If n is less than 5 and greater than or equal to -3, is n = 0 in the solution set?

• No, because 0 is less than -3

• Yes, because 0 is greater than 5

• No, because 0 is not between -3 and 5

• Yes, because 0 is between -3 and 5

Which value is not in the solution set for n < 5 and n ≥ -3?

• n = 5

• n = 0

• n = -3

• n = 4.99

How would you express a number greater than or equal to 5 but less than 8 as a compound inequality?

• n > 5 and n ≤ 8

• 5 ≤ n ≤ 8

• n ≥ 5 and n < 8

• 5 < n < 8

What is the maximum amount of gas a car's tank can hold if it ranges from 0 to 20 gallons?

• 10 gallons

• 15 gallons

• 20 gallons

• 25 gallons

If G represents gallons of gas, how would you write the inequality for a tank that can hold between 0 and 20 gallons?

• 0 ≤ G < 20

• 0 < G < 20

• G ≥ 0 and G ≤ 20

• G > 0 and G < 20

What does it mean if an interval is closed on one end and open on the other?

• Both endpoints are included

• Neither endpoint is included

• One endpoint is included, the other is not

• The interval is infinite