Solving Multi-Step Inequalities

The video tutorial covers solving multi-step inequalities, similar to multi-step equations, but with a range of answers. It explains how to express solutions in set builder and interval notation. The tutorial walks through two problems, demonstrating the use of distributive, addition, and division properties, and highlights the importance of flipping the inequality sign when dividing by a negative number. The video also emphasizes expressing solutions in both interval and set builder notation, and addresses the difference when the variable is on the right side of the inequality.

What is the first step in solving a multi-step inequality?

• Combine like terms

• Distribute through the parentheses

• Divide both sides by a number

• Add a constant to both sides

After distributing -4 in the first problem, what is the resulting expression?

• 6 - 24n + 28 >= 122

• 6 - 24n - 28 >= 122

• 6 - 24n - 28 > 122

• 6 + 24n - 28 >= 122

What property is used to combine 6 and -28 in the first problem?

• Distributive Property

• Combining Like Terms

• Addition Property

• Subtraction Property

What happens to the inequality sign when you divide both sides by a negative number?

• It stays the same

• It flips direction

• It becomes an equal sign

• It disappears

In interval notation, how is the solution n <= 6 expressed?

• (-∞, 6]

• (-∞, 6)

• [6, ∞)

• (6, ∞)

What is the main difference in the second problem compared to the first?

• There are no parentheses

• The variable is on the right side

• There are no constants

• The variable is on the left side

What is the result after subtracting 42 from both sides in the second problem?

• -180 >= -36b

• -180 <= -36b

• -180 > -36b

• -180 = -36b

How do you express the solution b >= 5 in interval notation?

• [5, ∞)

• (5, ∞)

• (-∞, 5)

• (-∞, 5]

In set builder notation, how is the solution b >= 5 expressed?

• {b | b <= 5}

• {b | b > 5}

• {b | b >= 5}

• {b | b < 5}

What should you do after watching the video and solving the practice problem?

• Move on to the next video

• Check your answer with the provided note

• Ask the teacher for help

• Skip the practice problem