Solving Compound Inequalities: Key Concepts and Techniques

This video tutorial covers lesson 2.5 on solving compound inequalities. It explains the types of compound inequalities, learning targets, and success criteria. The video provides detailed explanations and examples of compound inequalities, including set builder and interval notation. It also demonstrates methods for solving these inequalities and applies them to real-world problems. The lesson concludes with a summary and assignments for students.

What are the two types of compound inequalities?

• Joined by 'either' and 'neither'

• Joined by 'if' and 'then'

• Joined by 'but' and 'nor'

• Joined by 'and' and 'or'

What does the graph of a compound inequality with 'and' represent?

• The sum of the graphs of the inequalities

• The union of the graphs of the inequalities

• The difference of the graphs of the inequalities

• The intersection of the graphs of the inequalities

In set builder notation, how would you represent the inequality '2 ≤ x < 5'?

• {x | x < 2 and x ≥ 5}

• {x | x ≤ 2 or x > 5}

• {x | 2 ≤ x < 5}

• {x | 2 < x ≤ 5}

How would you write the interval notation for the inequality '−8 < x ≤ 4'?

• (-8, 4]

• [-8, 4)

• (-8, 4)

• [−8, 4]

What is the solution to the compound inequality '−2 < x < 5'?

• x > −2 and x < 5

• x ≤ −2 and x ≥ 5

• x ≥ −2 or x ≤ 5

• x < −2 or x > 5

When solving a compound inequality, what must you remember to do if you divide by a negative number?

• Keep the inequality sign the same

• Add the number to both sides

• Subtract the number from both sides

• Flip the inequality sign

What does the interval notation '(-∞, -1) ∪ (3, ∞)' represent?

• x ≤ -1 and x ≥ 3

• x < -1 or x > 3

• x ≤ -1 or x ≥ 3

• x < -1 and x > 3

In the real-world problem, what is the operating temperature range of the smartphone in Fahrenheit?

• 0 to 35 degrees

• 32 to 95 degrees

• 0 to 100 degrees

• 32 to 100 degrees

What formula is used to convert Celsius to Fahrenheit in the real-world problem?

• F = (C × 9/5) + 32

• C = (F − 32) × 5/9

• F = (C × 5/9) + 32

• C = (F + 32) × 9/5

What is the first step in solving the real-world problem involving the smartphone's operating temperature?

• Add 32 to both sides

• Multiply by 9/5

• Subtract 32 from both sides

• Divide by 5/9