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

Question

(5 points)
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) responses
multiplication of equality
addition of equality
subtraction of equality
distributive
division of equality
infinite no
one
combining like terms

(resulting equations) responses
x = 8
8 = 8
x = 0
16 = 8
2x + 8 = 2x +8
x + 16 = 2x + 8
2x + 16 = 2x + 8
x = 16

(step 3: types of solutions) responses
no
infinite
one

Answer 1

To solve the equation \( 2(x+8) = 2x + 8 \), let's follow the steps as requested.

Step 1

Use the Distributive Property to get the resulting equation.

When we distribute the \(2\) on the left side, we get: \[ 2x + 16 = 2x + 8 \]

Step 2

Use the Subtraction of Equality Property to get the resulting equation.

Subtracting \(2x\) from both sides gives us: \[ 16 = 8 \]

Step 3

There is/are no solution(s) because the statement \(16 = 8\) is a contradiction, meaning the equation has no solutions.

Final Answers

1. Step 1: Distributive Property → Resulting equation: \( 2x + 16 = 2x + 8 \)
2. Step 2: Subtraction of Equality Property → Resulting equation: \( 16 = 8 \)
3. There is/are no solution(s).