Question

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

Sure! Let me assist you in providing the reasons for each step in solving the equation \( 24(34+x) = 1,200 \).

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

Reason: Distributive Property was applied to expand the left-hand side of the equation. \( 24 \times 34 = 816 \), so the equation becomes \( 816 + 24x = 1,200 \).

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

Reason: Subtraction property of equality was used to isolate the term containing \( x \) on one side of the equation. Specifically, \( 816 \) is subtracted from both sides to maintain balance.

Step 3: \( 24x = 384 \)

Reason: Simplification was done after performing the subtraction in Step 2. The right side \( 1,200 - 816 \) simplifies to \( 384 \), yielding the equation \( 24x = 384 \).

Step 4: \( x = 16 \)

Reason: Division property of equality was applied by dividing both sides of the equation by \( 24 \) to isolate \( x \). So, \( x = \frac{384}{24} = 16 \).

Feel free to ask if you need more assistance!

Answer 2

what's the answer to Step 3: 24x=384

Multiplication as the inverse operation to isolate the variable
Combine like terms
Addition as the inverse operation to isolate the variable

Answer 3

The correct reason for Step 3: \( 24x = 384 \) is "Addition as the inverse operation to isolate the variable."

In this step, you eliminated the constant on the left side of the equation (the \( 816 \)) by subtracting it from both sides, which was shown in Step 2. Thus, the subsequent step leads to the equation simply being \( 24x = 384 \).

So the response you should select for Step 3 is:

Addition as the inverse operation to isolate the variable.

Please let me know if you need further clarification or assistance!