Question

Solve the equation justifying each step with the correct reasoning. 2(x+8)=2x+8

Step 1: Blank Property to get Blank simplified equation

Step 2: Blank Property to get Blank simplified equation

Answer 1

To solve the equation \( 2(x + 8) = 2x + 8 \), we will justify each step clearly.

**Step 1:** Apply the **Distributive Property** to get the simplified equation.

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

**Explanation:** The Distributive Property states that \( a(b + c) = ab + ac \). Here, multiplying 2 with both \( x \) and 8 results in \( 2x + 16 \).

Now the equation becomes:
\[
2x + 16 = 2x + 8
\]

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**Step 2:** Apply the **Subtraction Property of Equality** to get the simplified equation.

\[
16 = 8
\]

**Explanation:** The Subtraction Property of Equality states that if two expressions are equal, you can subtract the same value from both sides without changing the equality. In this case, we subtract \( 2x \) from both sides of the equation, leading us to \( 16 = 8 \).

At this point, we notice that \( 16 = 8 \) is not a true statement, indicating that the original equation has no solution.

**Conclusion:** Since we derived a false statement from the original equation, we conclude that there are no values of \( x \) that satisfy the equation \( 2(x + 8) = 2x + 8 \). Thus, the solution is that there is **no solution**.