In this lesson, Caitlin guides students through solving algebraic problems, focusing on understanding the impact of subtraction and parentheses in expressions. The video covers identifying and correcting errors in algebraic expressions, proving the equivalence of different expressions, and solving real-world problems using inequalities. Students learn to apply algebraic concepts to practical scenarios, such as budgeting and charity donations, enhancing their problem-solving skills.

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

• 15x

• 3x

• 11x

• 7x

In the process of simplifying an expression, what is a common mistake when dealing with negative signs?

• Ignoring the negative sign

• Combining terms incorrectly

• Changing all minuses to pluses

• Adding numbers without considering variables

What is the correct way to handle a negative sign in front of a group of terms?

• Change it to a positive sign

• Distribute it to all terms in the group

• Apply it to the first term only

• Ignore it

Which of the following expressions is equivalent to 5x - (15 + 20x) + 10?

• 5x + 15 - 20x + 10

• 5x - 15 + 20x - 10

• 5x + 15 + 20x - 10

• 5x - 15 - 20x + 10

What is the result of combining like terms in the expression 5x + 20x - 15?

• 25x - 15

• 25x + 15

• 15x + 15

• 15x - 15

Which method can be used to prove that different expressions are equivalent?

• Ignoring variables

• Factoring out common terms

• Changing all signs

• Adding random numbers

How much can the school spend on each uniform if the total budget is $750 and competition fees are $300?

• $30 or less

• $50 or less

• $20 or less

• $40 or less

What inequality represents the cost of uniforms if the budget is $750 and fees are $300?

• 15x + 300 ≤ 750

• 15x + 300 ≥ 750

• 15x - 300 ≥ 750

• 15x - 300 ≤ 750

If Elena wants to keep at least $42 from her earnings, how much can she donate per $9 earned?

• Exactly $3

• At most $3

• More than $3

• At least $3

If Elena donates $x per $9 earned, what inequality ensures she keeps at least $42?

• 7(9 - x) ≥ 42

• 7(9 - x) ≤ 42

• 7(9 + x) ≥ 42

• 7(9 + x) ≤ 42