Exploring Compound Inequalities

This lesson covers compound inequalities, which are two or more inequalities joined by 'and' or 'or'. It explains how to graph 'or' inequalities, which graph apart, and 'and' inequalities, which graph together. Examples are provided for both types, including how to simplify and solve inequalities before graphing. The lesson also covers rewriting 'and' inequalities in a condensed form and solving more complex inequalities involving additional terms.

What is a compound inequality?

• An equation with no variables

• A single inequality with two variables

• Two or more inequalities joined together

• An equation with one variable

How do 'or' compound inequalities typically graph?

• On the same line

• In the same direction

• Together

• Apart

In the inequality x < -2 or x > 3, what type of points are used on the graph for -2 and 3?

• Open point for -2, closed point for 3

• Both closed points

• Closed point for -2, open point for 3

• Both open points

What does the inequality x < -3 or x ≥ 6 mean in terms of graphing?

• x can only be -3 or 6

• x can be any value greater than -3 and less than 6

• x can be any value less than -3 or greater than or equal to 6

• x can be any value between -3 and 6

How do 'and' compound inequalities typically graph?

• In opposite directions

• On different lines

• Apart

• Together

In the inequality -6 ≤ x ≤ 1, what does the graph look like?

• A line from -6 to 1 with closed points

• A single point at 0

• A line from -6 to 1 with open points

• Two separate lines

How can the inequality -6 ≤ x ≤ 1 be rewritten?

• x > -6 and x < 1

• x ≤ -6 and x ≥ 1

• x < -6 and x > 1

• x ≥ -6 and x ≤ 1

What is the first step in solving the inequality -2 ≤ x + 4 < 5?

• Divide each side by 4

• Multiply each side by 4

• Add 4 to each side

• Subtract 4 from each side

In the inequality -14 ≤ 7x < 21, what is the next step after simplifying the constants?

• Multiply each side by 7

• Subtract 7 from each side

• Divide each side by 7

• Add 7 to each side

What does the graph of -2 < x < 3 look like?

• Two separate lines

• A line from -2 to 3 with closed points

• A line from -2 to 3 with open points

• A single point at 0