Solve the equation using the property and the steps: 2 (x + 8) = 2x + 8

Question

Step 1: Response area Property to get Response area

Step 2: Response area Property to get Response area

There is/are Response area solution(s)

the response areas are the blanks utilize every response area you imbecile

Answer 1

To solve the equation \(2(x + 8) = 2x + 8\) using properties of equality and algebraic manipulation, let's break it down step by step.

Step 1: Apply the Distributive Property

We can apply the Distributive Property to the left side of the equation.

Response area: Distributive Property

Solution: Distributing \(2\) gives us:

\[ 2 \cdot x + 2 \cdot 8 = 2x + 16 \]

So the equation becomes:

\[ 2x + 16 = 2x + 8 \]

Step 2: Simplifying the Equation

Now, we want to isolate \(x\). To do this, we'll subtract \(2x\) from both sides.

Response area: Subtracting \(2x\) from both sides

Solution: This gives us:

\[ 16 = 8 \]

This simplifies to a false statement.

Conclusion

Since our manipulation led to a contradiction (16 does not equal 8), it indicates that there are no solutions to the original equation.

Response area: There are no solutions.

Thus, the final statement is:

There is/are no solution(s).