To solve the equation: 24(34+x)=1,200

Question

, give the reasons for each of the given steps.

What was done to the previous step to get to the current equation?

Step 2: 816 − 816 + 24x = 1,200 − 816

Answer 1

To solve the equation \( 24(34+x) = 1,200 \) with the provided second step, we can break down the steps and explain their reasoning.

Given Step 2

Step 2: \( 816 - 816 + 24x = 1,200 - 816 \)

Reasoning for the Step

1. Distributing the \( 24 \): In a previous step (which isn't shown), the equation likely underwent distribution.

   • Starting from \( 24(34+x) = 1,200 \), you would distribute the \( 24 \) to both terms inside the parentheses: \[ 24 \times 34 + 24 \times x = 1,200 \] This yields: \[ 816 + 24x = 1,200 \]

2. Isolating \( 24x \): The goal is to isolate \( 24x \) on one side of the equation. To do this, you can subtract \( 816 \) from both sides of the equation: \[ 816 + 24x - 816 = 1,200 - 816 \] This simplifies to: \[ 24x = 384 \] However, the notation used in Step 2 introduces \( -816 \) and \( +816 \) explicitly. The equation keeps the same relationship but emphasizes balancing the equation visually.

Summary of Reasoning

• Step 2 takes the equation \( 24(34+x) = 1,200 \) (after distributing) and transforms it into \( 816 + 24x = 1,200 \), then elements \( -816 \) are introduced to clarify the subtraction process and the balancing of both sides of the equation, leading to an equivalent situation which allows for easier solving.

Subsequent Steps

From here, you can move to solving for \( x \) by dividing both sides by 24 after rearranging to \( 24x = 384 \), eventually leading to \( x = 16 \).