Solving Compound Inequalities

The video tutorial covers compound inequalities, focusing on both AND and OR types. It explains how to graph these inequalities, highlighting the intersection for AND and the union for OR. The tutorial includes practice problems and detailed steps for solving compound inequalities, emphasizing the importance of reversing inequality symbols when necessary. The session concludes with a summary of key concepts and encourages viewers to subscribe for more lessons.

What is a compound inequality?

• An inequality that combines two inequalities using 'AND' or 'OR'

• An inequality that is always true

• An inequality that has no solution

• An inequality with only one variable

How is an 'AND' compound inequality represented on a graph?

• As a circle

• As a union of two graphs

• As a single line

• As an intersection of two graphs

What does the graph of x > -3 and x < 5 look like?

• A line from -3 to 5 with open circles at both ends

• A line from -3 to 5 with a closed circle at -3 and an open circle at 5

• A line extending infinitely in both directions

• A line from -3 to 5 with closed circles at both ends

What is the key feature of an 'OR' compound inequality graph?

• It has no solution

• It is always a single line

• It shows the union of two solution sets

• It shows the intersection of two solution sets

Which of the following is a correct representation of x < -1 or x > 2?

• Two separate lines, one extending left from -1 and one extending right from 2

• A line from -1 to 2 with closed circles at both ends

• A line from -1 to 2 with open circles at both ends

• A single line from -1 to 2

How do you solve an 'AND' compound inequality?

• By solving each inequality separately and finding their intersection

• By solving only one of the inequalities

• By graphing both inequalities on the same number line

• By solving each inequality separately and finding their union

What is the solution to the compound inequality -5 ≤ -4x + 3 ≤ 11?

• x ≥ 2 and x ≤ -2

• x ≤ -2 and x ≥ 2

• x ≤ 2 and x ≥ -2

• x ≥ -2 and x ≤ 2

How do you solve an 'OR' compound inequality?

• By solving only one of the inequalities

• By graphing both inequalities on the same number line

• By solving each inequality separately and finding their union

• By solving each inequality separately and finding their intersection

What is the solution to the compound inequality 5x ≤ -10 or 2x > 7?

• x ≤ -2 or x > 3.5

• x ≥ 2 or x < -3.5

• x ≥ -2 or x < 3.5

• x ≤ 2 or x > -3.5

What does the graph of x < -5 or x ≥ 2 look like?

• A single line from -5 to 2

• A line from -5 to 2 with open circles at both ends

• Two separate lines, one extending left from -5 and one extending right from 2

• A line from -5 to 2 with closed circles at both ends