Solving Compound Inequalities

This video tutorial explains how to solve compound inequalities using additive and multiplicative inverses. It covers the difference between 'or' and 'and' inequalities, demonstrating how to solve each type. The tutorial includes examples and checks to ensure solutions are correct, emphasizing the importance of understanding the logical operators 'or' and 'and' in inequalities.

What is the first step in solving the inequality 3x > 2x + 7?

• Divide both sides by x

• Multiply both sides by 3

• Subtract 2x from both sides

• Add 7 to both sides

When solving inequalities with the word 'or', what must be true about the solutions?

• They must be equal to each other

• They must satisfy at least one inequality

• They must satisfy both inequalities

• They must be greater than zero

In the inequality -2x + 7 < 5x, what is the solution for x?

• x < 1

• x > 1

• x > -3

• x < -3

What is the solution for x in the inequality 4x < -12?

• x > 3

• x < 3

• x > -3

• x < -3

When solving inequalities with the word 'and', what must be true about the solutions?

• They must satisfy both inequalities

• They must satisfy at least one inequality

• They must be less than zero

• They must be equal to each other

What is the solution for a in the inequality 5a + 2 < 7?

• a < 1

• a > -1

• a < -1

• a > 1

What is a common mistake when interpreting compound inequalities?

• Misunderstanding 'or' and 'and' conditions

• Forgetting to multiply by the inverse

• Using the wrong variable

• Not checking the solution