Question

The model below represents 4 x + (negative 4) = negative 2 x + 8.

4 long green tiles and 4 square red tiles = 2 long red tiles and 8 square green tiles.

What is the value of x when solving the equation 4 x + (negative 4) = negative 2 x + 8 using the algebra tiles?
x = negative 4
x = negative 2
x = 2
x = 4

Answer 1

To solve the equation \( 4x - 4 = -2x + 8 \) using algebra tiles, we can rearrange and combine like terms step by step.

1. **Start with the equation**:
\[
4x - 4 = -2x + 8
\]

2. **Add \( 2x \) to both sides** to get all the \( x \) terms on one side:
\[
4x + 2x - 4 = 8
\]
Which simplifies to:
\[
6x - 4 = 8
\]

3. **Add \( 4 \) to both sides** to isolate the \( x \) terms:
\[
6x - 4 + 4 = 8 + 4
\]
Which simplifies to:
\[
6x = 12
\]

4. **Divide both sides by \( 6 \)** to solve for \( x \):
\[
x = \frac{12}{6} = 2
\]

Thus, the solution to the equation is \( x = 2 \).

Therefore, the correct answer is:
\[
\boxed{2}
\]