Fatima was asked to use attendant identify appropriate properties of equality to find the value of why that makes the statement 3/4 (y+ 8) = 1/2 (2y + 4)true show the properties used

Answer 1

To solve the equation \( \frac{3}{4}(y + 8) = \frac{1}{2}(2y + 4) \) and identify the properties of equality used, we can follow these steps:

1. Distribute on both sides: \[ \frac{3}{4}y + \frac{3}{4} \cdot 8 = \frac{1}{2} \cdot 2y + \frac{1}{2} \cdot 4 \] This involves using the Distributive Property.

2. Simplify both sides: \[ \frac{3}{4}y + 6 = y + 2 \]

3. Subtract \( y \) from both sides: \[ \frac{3}{4}y - y + 6 = 2 \] This uses the Subtraction Property of Equality.

4. Rewrite \( y \) on the left-hand side: \[ \frac{3}{4}y - \frac{4}{4}y + 6 = 2 \] Which simplifies to: \[ -\frac{1}{4}y + 6 = 2 \]

5. Subtract 6 from both sides: \[ -\frac{1}{4}y = 2 - 6 \] This again uses the Subtraction Property of Equality.

6. Simplifying gives: \[ -\frac{1}{4}y = -4 \]

7. Multiply both sides by -4 (the reciprocal of \(-\frac{1}{4}\)): \[ y = -4 \cdot -4 \] Which is applying the Multiplication Property of Equality.

8. Finally, solving this gives: \[ y = 16 \]

The properties used in the solution are:

• Distributive Property (Step 1)
• Subtraction Property of Equality (Steps 3 and 5)
• Multiplication Property of Equality (Step 7)

So, the value of \( y \) that makes the original equation true is \( 16 \).