In this video, Caitlin guides students through several algebraic problems, focusing on expressions and inequalities. The lesson begins with a discussion on simplifying expressions and identifying errors in algebraic manipulations. Caitlin then demonstrates how to prove the equivalence of different expressions. The video also covers practical applications of algebra, such as solving budgeting and charity donation problems using inequalities. Throughout the lesson, Caitlin emphasizes the importance of understanding the role of parentheses and signs in expressions.

What is the correct simplification of the expression 9x - 2x + 4x?

• 11x

• 3x

• 7x

• 5x

In the expression simplification, when does a minus sign affect more than one term?

• When at the start of an expression

• When followed by parentheses

• When followed by a number

• When followed by a variable

What was the error made in simplifying the expression involving negative numbers?

• Distributing incorrectly

• Adding extra terms

• Combining terms incorrectly

• Ignoring the negative sign

How should the expression 4 + (-5) be correctly written?

• 4 - 5

• 5 + 4

• 5 - 4

• 4 + 5

Which of the following is a valid way to prove expression equivalence?

• Adding random numbers

• Factoring out common terms

• Ignoring variables

• Changing all signs

What is the maximum cost per uniform if the total budget is $750 and competition fees are $300?

• $25

• $20

• $35

• $30

How many uniforms can be purchased if each costs $30 and the budget is $450?

• 10

• 20

• 12

• 15

What is the inequality representing Elena's charity donation scenario?

• 7(9 + x) ≥ 42

• 7(9 - x) ≤ 42

• 7(9 - x) ≥ 42

• 7(9 + x) ≤ 42

If Elena wants to keep at least $42, what is the maximum amount she can donate per $9 earned?

• $5

• $2

• $3

• $4

What should be done if the inequality sign is flipped during solving?

• Ignore the change

• Recalculate the entire problem

• Adjust the inequality direction

• Add a constant to both sides