Question

Question

Solve the equation using the steps: 2(x+8)=2x+8
(5 points)
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Step 1: Use the Response area Property to get Response area resulting equation.

Step 2: Use the Response area Property to get Response area resulting equation.

Step 3: There is/are Response area solution(s).

Properties
No, One, Combining Like Terms, Division Of Equality, Addition of Equality, Subtraction of Equality, Infinite, Distributive, Multiplication of Equality
Resulting Equations
2x + 16 = 2x +8, x + 16 = 2x + 8 16=8, x = 8, x =16, 2x + 8 = 2x + 8, x = 0, 8 = 8
Step 3: Types of Solutions
No, One, Infinite

Answer 1

Let's solve the equation step by step, using the provided properties and resulting equations.

Given Equation:

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

Step 1:

First, we will apply the Distributive Property to simplify the left side of the equation:

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

Resulting equation: \[ 2x + 16 = 2x + 8 \]

• Response area Property: Distributive
• Resulting Equation: 2x + 16 = 2x + 8

Step 2:

Next, we will apply the Subtraction of Equality to eliminate \(2x\) from both sides:

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

Resulting equation: \[ 16 = 8 \]

• Response area Property: Subtraction of Equality
• Resulting Equation: 16 = 8

Step 3:

The equation \(16 = 8\) is a contradiction, indicating that there are no solutions.

• There is/are: No

Summary of Responses:

• Step 1: Distributive, Resulting Equation: 2x + 16 = 2x + 8
• Step 2: Subtraction of Equality, Resulting Equation: 16 = 8
• Step 3: There is/are: No

This means the final solution reflects that the original equation has no solution.