Let's analyze each step of the solution to the equation \( 24(34+x) = 1,200 \) and provide the reasoning for each step based on the options given.
Step 1: \( 816 + 24x = 1,200 \)
This step involves expanding the left side of the equation:
- Reason: This is where you distribute the \( 24 \) across the parentheses. \[ 24(34) + 24(x) = 816 + 24x \]
Step 2: \( 816 - 816 + 24x = 1,200 - 816 \)
Here, \( 816 \) is subtracted from both sides of the equation:
- Reason: This step is applying the property of equality, specifically using Addition as the inverse operation to isolate the variable \( x \). By moving \( 816 \) to the other side, the equation is simplified: \[ 24x = 1,200 - 816 \]
Step 3: \( 24x = 384 \)
In this step, the right side of the equation is simplified:
- Reason: Combine Like Terms. The subtraction \( 1,200 - 816 \) results in \( 384 \), thereby simplifying the equation further.
Step 4: \( x = 16 \)
This step involves isolating \( x \) by dividing both sides by \( 24 \):
- Reason: This step uses Division as the inverse operation to isolate the variable \( x \). Thus, \[ x = \frac{384}{24} = 16 \]
Summary of Steps with corresponding reasons:
- Step 1: Distribution (Expansion)
- Step 2: Addition as the inverse operation to isolate the variable
- Step 3: Combine Like Terms
- Step 4: Division as the inverse operation to isolate the variable
The correct options for the reasons are:
- Step 2: 3. Addition as the inverse operation to isolate the variable
- Step 3: 2. Combine Like Terms
- Step 4: 4. Division as the inverse operation to isolate the variable
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