Question

To solve the equation: 24 (34+x)= 1,200, give the reasons for each of the given steps. What was done to the previous step to get to the current equation?

Step 1: 816+24x=1,200

Step 2: 816−816+24x=1,200 − 816

Step 3: 24x=384

Step 4: x=16

answers

multiplication as the inverse operation to isolate the variable

distributive property

subtract as the inverse operation to isolate variable

combine like terms

addition as the inverse operation to isolate the variable

division as the inverse operation to isolate the variable

Answer 1

Let's break down each of the steps in your solution to the equation \( 24(34 + x) = 1,200 \) and explain what was done to arrive at each step, along with the corresponding reasoning from the provided answers.

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

**Reasoning**: Distributive property
**Explanation**: In this step, we applied the distributive property to expand the left side of the equation. Specifically, we multiplied \( 24 \) by both \( 34 \) and \( x \):
\[
24(34) + 24(x) = 1,200 \implies 816 + 24x = 1,200.
\]

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

**Reasoning**: Subtract as the inverse operation to isolate the variable
**Explanation**: Here, we subtract \( 816 \) from both sides of the equation to move the constant term to the right side. This helps us to isolate the term containing \( x \):
\[
816 - 816 + 24x = 1,200 - 816 \implies 0 + 24x = 384.
\]

### Step 3: \( 24x = 384 \)

**Reasoning**: Combine like terms
**Explanation**: After the subtraction in Step 2, we simplify the equation. Since \( 0 + 24x \) is just \( 24x \), we have:
\[
24x = 384.
\]

### Step 4: \( x = 16 \)

**Reasoning**: Division as the inverse operation to isolate the variable
**Explanation**: Finally, to solve for \( x \), we divide both sides of the equation by \( 24 \) to isolate \( x \):
\[
x = \frac{384}{24} \implies x = 16.
\]

### Summary
1. **Step 1**: Distributive property
2. **Step 2**: Subtract as the inverse operation to isolate the variable
3. **Step 3**: Combine like terms
4. **Step 4**: Division as the inverse operation to isolate the variable

This step-by-step breakdown illustrates the methods used at each stage in solving the equation and aligns reasoning with the specific operations performed.