Identify the equation that is solved correctly given the following written directions: subtract 5 from both sides of the equation. Then, multiply both sides of the equation by negative 2. The final answer is x = 8.

Answer 1

Let's denote the original equation as \( x \).

1. Starting with the original equation: We will call it \( x = A \), where \( A \) is the expression we will solve.
2. Subtract 5 from both sides: \[ x - 5 = A - 5 \]
3. Multiply both sides by -2: \[ -2(x - 5) = -2(A - 5) \]

Now, we need to isolate \( x \) in such a way that the final result gives \( x = 8 \).

Solving for the original equation:

Given that the final answer is \( x = 8 \), we set up the equation.

1. Starting from the final equation \( x = 8 \): \[ -2(x - 5) = -2(8 - 5) \ -2(x - 5) = -2(3) \ -2(x - 5) = -6 \]

2. Divide both sides by -2: \[ x - 5 = 3 \]

3. Add 5 to both sides: \[ x = 3 + 5 \ x = 8 \]

This confirms that the original equation before the modifications was: \[ x - 5 = 3 \]

Thus, if we rewrite:

• Original equation before these operations: \[ x = 3 + 5 \implies x = 8 \]

Confirming the transformations:

1. Subtracting 5: \[ x - 5 = 3 \]
2. Multiplying through by -2: \[ -2(x - 5) = -6 \implies -2x + 10 = -6 \implies -2x = -16 \implies x = 8 \]

Final Answer:

The original equation was: \[ x - 5 = 3 \] This correctly leads us to the final answer \( x = 8 \) when following the given instructions.