Question

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

Answer 1

To solve the equation \(-2x - 8 = 2x + 8\) for \(x\), let's first simplify and isolate \(x\) using algebraic steps.

1. **Combine like terms**: Add \(2x\) to both sides to eliminate \(x\) on the left side.
\[
-2x + 2x - 8 = 2x + 2x + 8
\]
This simplifies to:
\[
-8 = 4x + 8
\]

2. **Isolate the term with \(x\)**: Subtract \(8\) from both sides.
\[
-8 - 8 = 4x + 8 - 8
\]
This simplifies to:
\[
-16 = 4x
\]

3. **Solve for \(x\)**: Divide both sides by \(4\).
\[
x = \frac{-16}{4} = -4
\]

So the value of \(x\) is \(\mathbf{-4}\).

From the choices provided:
- **x = negative 4** (This is correct)
- x = negative 2
- x = 2
- x = 4

Thus, the correct answer is \(x = -4\).