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Solve the equation using the steps:

2 ( x + 8 ) = 2x + 8

Steps

Step 1. Use the () Property to get () resulting equation

Step 2. Use the () Property to get () resulting equation

Step 3. There is/are () solution(s)

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

1 answer

Let's solve the equation step by step:

Given Equation: \[ 2 ( x + 8 ) = 2x + 8 \]

Step 1: Use the Distributive Property to get resulting equation
Distributing \(2\) to both terms inside the parentheses: \[ 2x + 16 = 2x + 8 \]

Step 2: Use the Subtraction of Equality Property to get resulting equation
Subtract \(2x\) from both sides: \[ 16 = 8 \]

Step 3: There is/are No solution(s)
Since \(16 = 8\) is a false statement, the original equation has no solutions.

So, the filled steps are:

  • Step 1: Use the Distributive Property to get resulting equation: 2x + 16 = 2x + 8
  • Step 2: Use the Subtraction of Equality Property to get resulting equation: 16 = 8
  • Step 3: There is/are No solution(s)