Let's go through each step and provide the reason for each transformation based on the options given.
Step 1: 816 + 24x = 1,200
Reason: This step comes from using the Distributive Property.
- Explanation: The original equation is 24(34 + x) = 1,200. When you apply the distributive property, you multiply 24 by both 34 and x, which gives you 816 (since 24 * 34 = 816) and 24x. Thus, you arrive at: \[ 816 + 24x = 1200 \]
Step 2: 816 − 816 + 24x = 1,200 − 816
Reason: This step involves Subtracting as the inverse operation to isolate the variable.
- Explanation: To isolate the term involving x (which is 24x), you subtract 816 from both sides of the equation. This simplifies the equation while keeping it balanced. \[ 816 - 816 + 24x = 1,200 - 816 \]
Step 3: 24x = 384
Reason: This step is a result of Combining Like Terms.
- Explanation: In this step, you simplify the equation from Step 2 by combining the constant terms. The left side simplifies to just 24x (since 816 - 816 = 0), and on the right side, you compute 1,200 - 816, which equals 384. \[ 24x = 384 \]
Step 4: x = 16
Reason: This step uses Division as the inverse operation to isolate the variable.
- Explanation: To solve for x, you divide both sides of the equation by 24, which is the coefficient of x. By doing this, you isolate x on the left side of the equation. \[ x = \frac{384}{24} = 16 \]
Now assigning the reasons to the original steps:
- Step 1: 5. Distributive Property
- Step 2: 6. Subtracting 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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