Let's analyze each step and provide the reasons for them:
Step 1: 816 + 24x = 1,200
Reason: This simplification comes from distributing 24 across the parentheses in the original equation: 24(34 + x) = 1,200 becomes 2434 + 24x = 1,200. Calculating 24 * 34 results in 816.
Step 2: 816 - 816 + 24x = 1,200 - 816
Reason: We are isolating the term with the variable (24x) on one side by subtracting 816 from both sides of the equation. This maintains the equality (the balance of the equation).
Step 3: 24x = 384
Reason: This step follows from simplifying the previous equation: 816 - 816 cancels out to 0, leaving just 24x on the left side, and on the right side, we compute 1,200 - 816 to get 384.
Step 4: x = 16
Reason: This step involves solving for x by dividing both sides of the equation by 24. This operation isolates x on one side, giving the final solution. Thus, 384 divided by 24 equals 16.
In summary, each step involves either distribution, maintaining balance through subtraction, simplifying the equation, or isolating the variable through division to arrive at the solution.