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?

• 7x

• 5x

• 3x

• 11x

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

• When followed by a number

• When followed by a variable

• When followed by parentheses

• When at the start of an expression

What was the error made in the expression simplification that led to an incorrect result of -1?

• Incorrectly adding numbers

• Using the wrong operation

• Ignoring the x terms

• Combining like terms incorrectly

How should the expression 4 + (-5) + 2x + 2x be correctly simplified?

• -1 + 4x

• 1 + 4x

• 5 + 4x

• 0 + 4x

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

• Ignoring coefficients

• Changing variables

• Factoring out common terms

• Adding constants

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

• $35

• $30

• $25

• $20

How is the inequality for the uniform budget problem set up?

• 15x + 300 ≥ 750

• 15x - 300 ≥ 750

• 15x + 300 ≤ 750

• 15x - 300 ≤ 750

If Elena wants to keep at least $42, how much can she give to charity per $9 earned?

• At least $3

• At most $3

• Exactly $3

• More than $3

What inequality represents Elena's situation if she gives x dollars to charity?

• 7(9 - x) ≥ 42

• 7(9 + x) ≤ 42

• 7(9 - x) ≤ 42

• 7(9 + x) ≥ 42

Why might the inequality in Elena's problem need to be flipped?

• To make x positive

• To ensure she keeps more than $42

• To simplify the expression

• Because x is negative