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?

(4 points)
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Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
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Answer 1

Certainly! Let's break down the steps and provide the reasons for each transition in solving the equation \(24(34 + x) = 1,200\).

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

Reason: The equation \(24(34 + x)\) was distributed. When you multiply \(24\) by \(34\), you get \(816\), and that gives you the equation \(816 + 24x = 1,200\).

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

Reason: Subtracting \(816\) from both sides to isolate the term with \(x\). This maintains the equality of the equation.

Step 3: \(24x = 384\)

Reason: Simplifying the right side of the equation. After subtracting \(816\) from \(1,200\), we find that \(1,200 - 816 = 384\).

Step 4: \(x = 16\)

Reason: Dividing both sides of the equation \(24x = 384\) by \(24\) to solve for \(x\). This isolates \(x\), yielding the final solution.

In summary:

• Step 1: Distribution.
• Step 2: Subtraction to isolate \(x\).
• Step 3: Simplification of the right-hand side.
• Step 4: Division to solve for \(x\).