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

Question

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 \(x = -4\).