Solving Compound 'AND' Inequalities

This video tutorial covers the concept of compound inequalities, focusing on intersections rather than unions. It explains how to use truth tables to understand logical statements and provides step-by-step instructions for solving and graphing compound inequalities. The tutorial includes examples and practice problems to reinforce learning, highlighting common mistakes and how to avoid them.

What is the term used to describe the relationship where both conditions in a compound inequality must be true?

• Union

• Intersection

• Conjunction

• Combination

In a truth table for compound inequalities, when is the intersection true?

• When one condition is true and the other is false

• When at least one condition is true

• When both conditions are false

• When both conditions are true

How do you combine two separate inequalities into a compound inequality?

• By adding the inequalities

• By subtracting the inequalities

• By using the word 'or'

• By using two inequality signs with the variable in the middle

What is the correct way to solve a compound inequality with three parts?

• Treat it like two separate inequalities and solve each part

• Ignore the middle part and solve the outer parts

• Treat it as a single equation

• Solve each part separately and then combine

When graphing a compound inequality, what does a bracket on the number line indicate?

• The inequality is not strict

• The inequality is strict

• The number is included

• The number is not included

What mistake did the teacher correct when solving the compound inequality?

• Combining the inequalities incorrectly

• Using the wrong inequality sign

• Multiplying instead of dividing

• Adding instead of subtracting

In the example where 2x + 3 is solved, what is the first step?

• Add 3 to both sides

• Multiply by 2

• Divide by 2

• Subtract 3 from all three sides

How do you handle fractions in compound inequalities?

• Add the denominator to all sides

• Subtract the denominator from all sides

• Multiply all sides by the denominator

• Divide all sides by the denominator

What does a closed circle on a graph represent in compound inequalities?

• A parenthesis

• A strict inequality

• A bracket

• An open interval

What is the final step in solving a compound inequality involving fractions?

• Multiply all sides by the numerator

• Subtract the numerator from all sides

• Divide all sides by the numerator

• Add the numerator to all sides