Question

is this correct? Solve the equation justifying each step with the correct reasoning. 2(x+8)=2x+8 (5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1: Property to get simplified equation Step 2: Property to get simplified equation For this equation, there is/are

Answer 1

Let's solve the equation \( 2(x + 8) = 2x + 8 \) step by step, justifying each action:

Step 1: Distribute

Property Used: Distribution Property

We apply the distributive property to the left-hand side:

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

Now the equation looks like this:

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

Step 2: Isolate the variable

Property Used: Subtraction Property of Equality

Next, we can subtract \( 2x \) from both sides to simplify:

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

This simplifies to:

\[ 16 = 8 \]

Step 3: Conclusion

This statement \( 16 = 8 \) is a contradiction, indicating that there is no solution to the equation.

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In summary:

• For Step 1, we used the Distribution Property.
• For Step 2, we used the Subtraction Property of Equality.

Thus, there is no solution to the equation since it leads to a false statement.