Let's break down each step of the equation \( 24(34+x)=1,200 \) with explanations for how we transition from one step to the next.
Step 1: \( 816 + 24x = 1,200 \)
Reason: We distributed \( 24 \) across the terms inside the parentheses. The computation \( 24 \times 34 = 816 \), so the left side of the equation becomes \( 816 + 24x \).
Step 2: \( 816 - 816 + 24x = 1,200 - 816 \)
Reason: We are isolating \( 24x \) on one side of the equation. We subtracted \( 816 \) from both sides to move the constant term to the right side. This maintains equality by performing the same operation on both sides.
Step 3: \( 24x = 384 \)
Reason: After simplifying the previous equation, we found that \( 1,200 - 816 = 384 \). Thus, we have isolated \( 24x \) on the left side and calculated the result on the right side.
Step 4: \( x = 16 \)
Reason: We divide both sides of the equation \( 24x = 384 \) by \( 24 \) to solve for \( x \). The division gives us \( x = \frac{384}{24} = 16 \).
By following these steps, we successfully solved the equation \( 24(34 + x) = 1,200 \).