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 Multiplication as the inverse operation to isolate the variableDistributive PropertySubtraction as the inverse operation to isolate the variableCombine Like TermsAddition as the inverse operation to isolate the variableDivision as the inverse operation to isolate the variableSkip to navigationPreviousNext

Answer 1

Here’s a breakdown of each step with the reasons for the transitions:

Step 1: 816 + 24x = 1,200

• Reason: Distributive Property
  (This step comes from applying the distributive property to the left side of the original equation \( 24(34+x) \), which results in \( 24 \cdot 34 + 24 \cdot x = 816 + 24x \).)

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

• Reason: Subtraction as the inverse operation to isolate the variable
  (In this step, 816 is subtracted from both sides of the equation to isolate the term containing \( x \).)

Step 3: 24x = 384

• Reason: Combine Like Terms
  (This step results from simplifying the right side of the equation \( 1,200 - 816 \) which equals 384.)

Step 4: x = 16

• Reason: Division as the inverse operation to isolate the variable
  (Finally, to solve for \( x \), both sides of the equation are divided by 24, isolating \( x \).)

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