Question

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 \( 16 \).