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) where y = -20 show the properties used

Answer 1

To solve the equation \( \frac{3}{4} (y + 8) = \frac{1}{2} (2y + 4) \) and determine if \( y = -20 \) is a solution, we can follow the steps of solving the equation while identifying the properties of equality used.

### Step 1: Substitute \( y = -20 \)

We substitute \( y \) with \(-20\) into the equation:

\[
\frac{3}{4} (-20 + 8) = \frac{1}{2} (2(-20) + 4)
\]

### Step 2: Simplify both sides

- **Left Side:**

\[
-20 + 8 = -12
\]

Now substitute:

\[
\frac{3}{4} (-12) = -9
\]

- **Right Side:**

\[
2(-20) + 4 = -40 + 4 = -36
\]

Now substitute:

\[
\frac{1}{2} (-36) = -18
\]

### Step 3: Compare both sides

After simplification we have:

\[
-9 \neq -18
\]

### Conclusion

Since \(-9\) does not equal \(-18\), \( y = -20 \) is not a solution for the equation \( \frac{3}{4} (y + 8) = \frac{1}{2} (2y + 4) \).

### Properties of Equality Used

1. **Substitution Property**: This allows us to replace \( y \) with \(-20\) in the equation.
2. **Addition Property of Equality**: Used when simplifying expressions (e.g., combining like terms).
3. **Multiplication Property of Equality**: Used to multiply the simplified values by constants (e.g., multiplying by \( \frac{3}{4} \) and \( \frac{1}{2} \)).
4. **Reflexive Property**: If we were to analyze terms on each side independently, we could apply this property to establish equality through set values.

Thus, \( y = -20 \) does not satisfy the original equation.