Question

Complete the proof below.

Given: x + 11 = 2x - 54
Prove: x = 35
Reason?

A) Subtract 11 from both sides of the equation.
B) Add 54 to both sides of the equation.
C) Divide both sides of the equation by 2.
D) No reason, the proof is incomplete.

Answer 1

To prove that x = 35, add 54 to both sides of the equation and subtract 11, following standard algebraic procedures. The solution involves algebraic manipulation and rearrangement of the given linear equation.

Step-by-step explanation:

The question involves solving for x in the provided equation, x + 11 = 2x - 54, to prove that x = 35. To solve the equation, we can use algebraic steps that involve both sides of the equation:

1. 
   
3. 
   

Steps 2 and 3 respond to the multiple choice options provided in the question (B and A), aligning with standard algebraic procedures.

Therefore, the correct answer is:

• B) Add 54 to both sides of the equation.
• A) Subtract 11 from both sides of the equation.
• And then, as not formally listed in the steps, simplify the equation to find that x = 35, completing the proof.