Q29 Fatima was asked to use and identify appropriate properties of equality to find the value of y that makes the statement ¾ (y + 8) = ½ (2y + 4) true. She has written out her steps below. Label those steps with the property used.

Question

4 (¾ (y + 8)) = 4(½ (2y + 4)) (________________)
3 (y + 8) = 2y + 4 (simplify)
3(y) + 3(8) = 2y + 4 (____________________)
3y + 24 = 2y + 4 (simplify)
3y – 2y + 24 = 2y – 2y + 4 (_________________)
y + 24 = 4 (combine like terms)
y + 24 – 24 = 4 – 24 (_____________________)
y = -20

Answer 1

Here are the labeled steps with the appropriate properties of equality:

1. 4 (¾ (y + 8)) = 4(½ (2y + 4)) (Multiplication Property of Equality)

   • This property states that if you multiply both sides of an equation by the same number, the two sides remain equal.

2. 3 (y + 8) = 2y + 4 (Simplify)

   • This step simplifies the left-hand side and right-hand side after distributing the 4.

3. 3(y) + 3(8) = 2y + 4 (Distributive Property)

   • This property states that a(b + c) = ab + ac, which is applied when distributing 3 to both terms inside the parentheses.

4. 3y + 24 = 2y + 4 (Simplify)

   • This step simplifies the expression after distribution.

5. 3y – 2y + 24 = 2y – 2y + 4 (Subtraction Property of Equality)

   • This property states that you can subtract the same amount from both sides of an equation without changing the equality.

6. y + 24 = 4 (Combine like terms)

   • This simplifies the left side by combining like terms.

7. y + 24 – 24 = 4 – 24 (Subtraction Property of Equality)

   • Again, this property is used to subtract 24 from both sides of the equation.

This should correctly label the steps with the respective properties of equality used.