Solve the equation justifying each step with the correct reasoning.

Question

2 (x+8) = 2x + 8

give me the 2 steps and the 2 property's to get

for this equation there is/are ___________

Answer 1

To solve the equation \( 2(x + 8) = 2x + 8 \), we will go through the following steps:

Step 1: Distribute the 2 on the left side.

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

This simplifies to:

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

Reasoning: This step uses the Distributive Property, which states that \( a(b + c) = ab + ac \).

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Step 2: Subtract \( 2x \) from both sides.

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

This simplifies to:

\[ 16 = 8 \]

Reasoning: This step uses the Subtraction Property of Equality, which states that if you subtract the same value from both sides of an equation, the equality is still maintained.

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After performing these steps, we find that the resulting statement \( 16 = 8 \) is not true.

Thus, for this equation there are no solutions (it is inconsistent) since the simplified form leads to a false statement.

Answer 2

step 1 is _______________ property to get ______________

step 2 is_______________ property to get_______________

Answer 3

Sure! Here are the steps filled in as per your request:

Step 1: Distributing the \(2\) is the Distributive Property to get

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

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Step 2: Subtracting \(2x\) from both sides is the Subtraction Property of Equality to get

\[ 16 = 8. \]

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This indicates that the equation has no solution, as \(16\) does not equal \(8\).

Answer 4

so the answe is 16 =8?

Answer 5

No, the equation \(16 = 8\) is not a valid solution; instead, it is a false statement. The presence of \(16 = 8\) indicates that the original equation \(2(x + 8) = 2x + 8\) does not hold true for any value of \(x\).

In other words, when you simplify the equation, you end up with a contradiction, which shows that there are no solutions to the original equation.

To summarize:

• The equation simplifies to \(16 = 8\), which is false.
• Therefore, the original equation has no solutions.