Question

Val says that the model below represents the equation Negative 2 x + 7 = 3 x + (negative 4).
Tia says that the model represents the equation 7 minus 2 x = (negative 4) + 3 x.

2 negative x tiles and 7 positive 1 tiles = 3 x tiles and 4 negative 1 tiles

Who is correct, Val or Tia?
Only Val is correct.
Only Tia is Correct.
Both Val and Tia are correct.
Neither Val nor Tia is correct.

Answer 1

To determine who is correct, let's analyze the models and the corresponding expressions given by Val and Tia.

1. **Val's equation:**
\(-2x + 7 = 3x - 4\)

2. **Tia's equation:**
\(7 - 2x = -4 + 3x\)

Next, we can analyze both equations.

### Val's Equation:
1. Start with Val's equation:
\[
-2x + 7 = 3x - 4
\]
2. Rearranging terms lets us combine like terms. First, add \(2x\) to both sides:
\[
7 = 3x + 2x - 4
\]
This simplifies to:
\[
7 = 5x - 4
\]
3. Now, add \(4\) to both sides:
\[
11 = 5x
\]
4. Finally, divide by \(5\):
\[
x = \frac{11}{5}
\]

### Tia's Equation:
1. Start with Tia's equation:
\[
7 - 2x = -4 + 3x
\]
2. Rearranging terms lets us combine like terms. First, add \(2x\) to both sides:
\[
7 = -4 + 3x + 2x
\]
This simplifies to:
\[
7 = -4 + 5x
\]
3. Now, add \(4\) to both sides:
\[
11 = 5x
\]
4. Finally, divide by \(5\):
\[
x = \frac{11}{5}
\]

### Conclusion:
Both equations simplify to the same result of \(x = \frac{11}{5}\). Therefore, both Val and Tia's models accurately represent the same equation.

The answer is: **Both Val and Tia are correct.**