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? (4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1: 816+24x=1,200 Step 2: 816−816+24x=1,200 − 816 Step 3: 24x=384 Step 4: x=16

Answer 1

Let's analyze each step and provide the reasons for them:

**Step 1: 816 + 24x = 1,200**
**Reason:** This simplification comes from distributing 24 across the parentheses in the original equation: 24(34 + x) = 1,200 becomes 24*34 + 24*x = 1,200. Calculating 24 * 34 results in 816.

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**Step 2: 816 - 816 + 24x = 1,200 - 816**
**Reason:** We are isolating the term with the variable (24x) on one side by subtracting 816 from both sides of the equation. This maintains the equality (the balance of the equation).

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**Step 3: 24x = 384**
**Reason:** This step follows from simplifying the previous equation: 816 - 816 cancels out to 0, leaving just 24x on the left side, and on the right side, we compute 1,200 - 816 to get 384.

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**Step 4: x = 16**
**Reason:** This step involves solving for x by dividing both sides of the equation by 24. This operation isolates x on one side, giving the final solution. Thus, 384 divided by 24 equals 16.

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In summary, each step involves either distribution, maintaining balance through subtraction, simplifying the equation, or isolating the variable through division to arrive at the solution.