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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?
Step 1: 816 + 24x = 1,200 ____________
Step 2: 816 - 816 + 24x = 1,200 - 816 ___________
Step 3: 24x = 384 __________
Step 4: x = 16 _________
Fill in the blanks
Options: Multiplication as the inverse operation to isolate the 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

3 answers

Let's fill in the blanks based on the steps provided:

Step 1: 816 + 24x = 1,200 (Distributive Property)
Reason: This step was reached by using the distributive property to expand the expression 24(34 + x) = 1,200 to 2434 + 24x = 1,200, which equals 816 + 24x = 1,200.

Step 2: 816 - 816 + 24x = 1,200 - 816 (Subtraction as the inverse operation to isolate the variable)
Reason: This step involves subtracting 816 from both sides of the equation to isolate the term containing the variable on one side.

Step 3: 24x = 384 (Combine Like Terms)
Reason: In this step, the left side remains the same (24x), and on the right side, 1,200 - 816 is simplified to 384 by combining like terms.

Step 4: x = 16 (Division as the inverse operation to isolate the variable)
Reason: Here, we divided both sides by 24 to solve for x, isolating the variable.

So, the filled-in blanks are:

  1. Distributive Property
  2. Subtraction as the inverse operation to isolate the variable
  3. Combine Like Terms
  4. Division as the inverse operation to isolate the variable
are you sure this is correct

Let's go through the steps again to ensure accuracy:

We started with the equation:

Equation: \( 24(34 + x) = 1,200 \)

Step 1: Expand using the Distributive Property.

  • Transformation: \( 24 \times 34 + 24 \times x = 1,200 \)
  • This simplifies to \( 816 + 24x = 1,200 \).

Step 2: Isolate the term with the variable \( x \) by subtracting 816 from both sides.

  • Transformation: \( 816 - 816 + 24x = 1,200 - 816 \)
  • This simplifies to \( 24x = 384 \).

Step 3: In the previous step, we already isolated \( 24x \). Now, we solve for \( x \) by dividing both sides by 24.

  • Transformation: \( x = \frac{384}{24} \)
  • Which simplifies to \( x = 16 \).

Now with that breakdown, let’s clarify the reasons for each step:

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

  • Reason: The equation is expanded using the distributive property.

Step 2: \( 816 - 816 + 24x = 1,200 - 816 \) (Subtraction as the inverse operation to isolate the variable)

  • Reason: Subtracting 816 from both sides to isolate the term with \( x \).

Step 3: \( 24x = 384 \) (Combine Like Terms)

  • Reason: Simplifying the right side \( 1,200 - 816 \) which yields 384.

Step 4: \( x = 16 \) (Division as the inverse operation to isolate the variable)

  • Reason: Dividing both sides by 24 to solve for \( x \).

So the filled-in blanks are indeed correct as initially stated. Thank you for your patience. If you have any further questions or need clarification, feel free to ask!