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

Let's label the steps with the appropriate properties of equality used:

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

   • This step multiplies both sides of the equation by 4 to eliminate the fractions.

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

   • This step simplifies the left side after distributing the 4.

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

   • This step applies the distributive property to expand the left side.

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

   • This step simplifies from the previous equation.

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

   • This step subtracts 2y from both sides of the equation.

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

   • This step shows the result of combining like terms.

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

   • This step subtracts 24 from both sides of the equation.

This organizes the steps and correctly labels the properties used in Fatima's work.