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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)
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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

3 answers

Let's break down each step of the equation \( 24(34+x)=1,200 \) with explanations for how we transition from one step to the next.

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

Reason: We distributed \( 24 \) across the terms inside the parentheses. The computation \( 24 \times 34 = 816 \), so the left side of the equation becomes \( 816 + 24x \).

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

Reason: We are isolating \( 24x \) on one side of the equation. We subtracted \( 816 \) from both sides to move the constant term to the right side. This maintains equality by performing the same operation on both sides.

Step 3: \( 24x = 384 \)

Reason: After simplifying the previous equation, we found that \( 1,200 - 816 = 384 \). Thus, we have isolated \( 24x \) on the left side and calculated the result on the right side.

Step 4: \( x = 16 \)

Reason: We divide both sides of the equation \( 24x = 384 \) by \( 24 \) to solve for \( x \). The division gives us \( x = \frac{384}{24} = 16 \).

By following these steps, we successfully solved the equation \( 24(34 + x) = 1,200 \).

Chooses are multiplication as the inverse operation to isolate that variable, distributive property, subtraction as the inverse operation to isolate the variable, combine like terms, Addition as the inverse operation to isolate the variable, division as the inverse operation to isolate the variable

Let's connect your provided operations to the steps in solving the equation \( 24(34+x)=1,200 \) with the correct terminology. Here’s how we can appropriately label each step based on the operations you provided:

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

  • Operation: Distributive Property
  • Reason: We used the distributive property to simplify \( 24(34 + x) \) into \( 816 + 24x \).

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

  • Operation: Subtraction as the inverse operation to isolate the variable
  • Reason: We subtracted \( 816 \) from both sides to move \( 816 \) to the right side and isolate \( 24x \) on the left side.

Step 3: \( 24x = 384 \)

  • Operation: Combine like terms
  • Reason: After the subtraction, we simplified \( 1,200 - 816 \) to get \( 384\).

Step 4: \( x = 16 \)

  • Operation: Division as the inverse operation to isolate the variable
  • Reason: We divided both sides by \( 24 \) to solve for \( x \).

To summarize each step with the correct operation chosen, you can format it as follows:

  1. Distributive Property: \( 24(34+x) \) becomes \( 816 + 24x \).
  2. Subtraction as the inverse operation to isolate the variable: \( 816 \) is subtracted from both sides.
  3. Combine like terms: Simplifying \( 1,200 - 816 \) results in \( 384 \).
  4. Division as the inverse operation to isolate the variable: Dividing both sides by \( 24 \) gives \( x \).

This aligns the operations with the steps you provided for clarity in explaining how the equation was solved.