Inequalities and Expression Simplification

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.

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

• 11x

• 3x

• 7x

• 15x

In the process of simplifying an expression, what is the mistake if 2x and 2x are combined to make 0?

• They should be multiplied

• They should be subtracted to make 0

• They should be ignored

• They should be added to make 4x

When simplifying an expression, what should be done if a negative sign is in front of a group of terms?

• Distribute the negative sign to each term

• Ignore the negative sign

• Multiply all terms by zero

• Add the terms without the negative

Which of the following is a correct method to prove that two expressions are equivalent?

• Changing all signs to positive

• Ignoring the coefficients

• Factoring out a common term

• Adding random numbers

What is the result of factoring out a negative 5 from the expression 5x - 15 - 20x + 10?

• -5(x - 3 - 4x - 2)

• -5(x + 3 - 4x + 2)

• -5(x - 3 + 4x - 2)

• -5(-x + 3 - 4x + 2)

If a school has a budget of $750 for uniforms and competition fees total $300, what is the maximum cost per uniform if 15 uniforms are needed?

• $50

• $40

• $30

• $20

In the context of budgeting, what does it mean if an inequality states that the cost must be less than or equal to $30?

• The cost can be more than $30

• The cost must be exactly $30

• The cost can be $30 or less

• The cost must be less than $30

What is the first step in solving the inequality 15x + 300 ≤ 750?

• Add 300 to both sides

• Subtract 300 from both sides

• Multiply both sides by 15

• Divide both sides by 15

Elena wants to keep at least $42 from her earnings after donating to charity. If she earns $9 each time and donates x dollars, what is the maximum she can donate each time?

• $3

• $4

• $6

• $5

What is the correct interpretation of the inequality 7(9 - x) ≥ 42 in the context of Elena's earnings?

• Elena must donate exactly $3

• Elena must donate more than $6

• Elena can donate $3 or less

• Elena can donate more than $3