Solving and Graphing Compound Inequalities

This video tutorial covers compound inequalities, focusing on those joined by 'or'. It explains the concept using truth tables and provides examples of how to solve and graph these inequalities. The tutorial also demonstrates how to write compound inequalities from graphs, emphasizing the importance of understanding the 'or' relationship. Key concepts include the use of truth tables, graphing techniques, and solving methods for compound inequalities.

What is a compound inequality?

• An equation with one inequality

• An equation with only 'or' inequalities

• An equation with two or more inequalities joined by 'and' or 'or'

• An equation with only 'and' inequalities

In a truth table, when is the statement 'P or Q' true?

• Only when both P and Q are true

• Only when both P and Q are false

• When either P or Q is true

• When neither P nor Q is true

What do we call the relationship where one or both statements are true?

• Intersection

• Union

• Difference

• Complement

Which of the following numbers is a solution to the inequality 'x < 2 or x > 6'?

• 4

• 5

• 7

• 3

How do you graph the inequality 'x < 2 or x > 6'?

• Two arrows pointing towards each other

• Two arrows pointing away from each other

• A single arrow pointing to the right

• A single arrow pointing to the left

What is the first step in solving the compound inequality '-4 + x > 1 or -4 + x < -3'?

• Subtract 4 from both sides

• Graph the inequalities

• Split them into two separate inequalities

• Combine the inequalities

What is the solution to the inequality '-4 + x > 1'?

• x > -3

• x < -3

• x > 5

• x < 5

When graphing 'x > 5 or x < 1', what should the graph look like?

• Two arrows pointing towards each other

• Two arrows pointing away from each other

• A single arrow pointing to the right

• A single arrow pointing to the left

What must you remember to do when dividing both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Keep the inequality sign the same

• Flip the inequality sign

What is the solution to the inequality '6x + 6 > 42'?

• x > 6

• x < 6

• x > 7

• x < 7