Ask a New Question
Menu

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

9 answers

Sure! Here's how to explain each step along with the reasoning for the operations performed:

Step 1: 816 + 24x = 1,200

  • Reason: This step involves distributing 24 into (34 + x). The multiplication is done first: \( 24 \times 34 = 816 \) and \( 24 \times x = 24x \), leading to the equation \( 816 + 24x = 1,200 \).

Step 2: 816 − 816 + 24x = 1,200 − 816

  • Reason: To isolate the term with x, we subtract 816 from both sides of the equation. This keeps the equation balanced, resulting in \( 24x = 1,200 - 816 \).

Step 3: 24x = 384

  • Reason: The subtraction simplifies the right-hand side of the equation \( 1,200 - 816 \) to 384. Now we have the simplified equation \( 24x = 384 \).

Step 4: x = 16

  • Reason: To solve for x, we divide both sides of the equation \( 24x = 384 \) by 24. This isolates x on the left side, resulting in \( x = \frac{384}{24} = 16 \).

Now every step along with the reasoning behind it is carefully explained!

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
responses
multiplication as the inverse operation to isolate the variable
subtraction as the inverse operation to isolate the variable
distributive property
combine like terms
addition as the inverse operation to isolate the variable
division as the inverse operation to isolate the variable

Here are the responses that correspond to each step in the solution of the equation, along with explanations:

Step 1: 816 + 24x = 1,200

  • Response: Distributive property
    • Explanation: The equation \( 24(34 + x) = 1,200 \) was solved by applying the distributive property to multiply 24 by both 34 and x, resulting in \( 24 \cdot 34 + 24 \cdot x = 1,200 \); this leads to \( 816 + 24x = 1,200 \).

Step 2: 816 − 816 + 24x = 1,200 − 816

  • Response: Subtraction as the inverse operation to isolate the variable
    • Explanation: To isolate the term with x on one side of the equation, 816 was subtracted from both sides, resulting in \( 24x = 1,200 - 816 \).

Step 3: 24x = 384

  • Response: Combine like terms
    • Explanation: The subtraction \( 1,200 - 816 \) is simplified to 384, resulting in the equation \( 24x = 384 \).

Step 4: x = 16

  • Response: Division as the inverse operation to isolate the variable
    • Explanation: To solve for x, both sides of the equation \( 24x = 384 \) were divided by 24, leading to \( x = \frac{384}{24} = 16 \).

You can fill in the responses according to the steps as outlined!

Simplify: −4(2x+5)
(1 point)
Responses

(−4×2x)+(−4×5)
open paren negative 4 times 2 x close paren plus open paren negative 4 times 5 close paren

(−4÷2x)+(−4÷5)
open paren negative 4 divided by 2 x close paren plus open paren negative 4 divided by 5 close paren

(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren

(−4−2x)+(−4−5)

To simplify the expression \( -4(2x + 5) \), we need to apply the distributive property. Here’s how it breaks down:

  1. Apply the distributive property: \( -4(2x + 5) = -4 \times 2x + -4 \times 5 \)

Based on the responses provided, the correct one to choose is:

(−4×2x)+(−4×5)

  • This shows the correct operation of distributing \(-4\) to both \(2x\) and \(5\).

Therefore, the simplified expression would be:

\(-8x - 20\)

The other options listed (division, addition, or incorrect grouping) are not appropriate for this expression.

Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(4 points)
responses
get constants together on one side: -26 = x
get x-terms together on one side: -16 = x + 10
distribute: -8x - 16 + 2x = -5x + 10
combine like terms: -6x - 16 = -5x + 10

To solve the equation \( -2(4x + 8) + 2x = -5x + 10 \), here are the steps in the correct order along with the associated responses:

  1. Distribute:
    Response: distribute: -8x - 16 + 2x = -5x + 10

    • Explanation: Apply the distributive property to \(-2(4x + 8)\), which gives you \(-8x - 16\).

  2. Combine like terms:
    Response: combine like terms: -6x - 16 = -5x + 10

    • Explanation: Combine the \(x\)-terms on the left side \(-8x + 2x = -6x\), maintaining the \(-16\).

  3. Get x-terms together on one side:
    Response: get x-terms together on one side: -16 = x + 10

    • Explanation: Add \(5x\) to both sides and rearrange the equation to move all \(x\)-terms to one side.

  4. Get constants together on one side:
    Response: get constants together on one side: -26 = x

    • Explanation: Finally, isolate \(x\) by subtracting \(10\) from both sides, leading to \(-26 = x\).

So the correct order is:

  1. Distribute: -8x - 16 + 2x = -5x + 10
  2. Combine like terms: -6x - 16 = -5x + 10
  3. Get x-terms together on one side: -16 = x + 10
  4. Get constants together on one side: -26 = x

This sequence leads to finding the value of \( x \).

A student solves the following problem: 2(x - 2) + 5x = 24

Step 1: 2x - 4 + 5x = 24

Step 2: 10x - 4 = 24

Step 3: 10x - 4 + 4 = 24 + 4

Step 4: 10x = 28

Step 5: 10x/10=28/10

Step 6: x = 2.8



Where is the mistake? What did the student do incorrectly?

(1 point)
Responses

Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 1: The student should have only distributed the 2 and x, not the x & -2.

Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.

Step 3: The student should have subtracted 4 from both sides, not added 4.
Step 3: The student should have subtracted 4 from both sides, not added 4.

Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.

The mistake in the student's solution happens in Step 2. Let's analyze it:

  1. In Step 1, the distribution is correct: \(2(x - 2) + 5x\) correctly becomes \(2x - 4 + 5x = 24\).

  2. However, in Step 2, the student incorrectly combined \(2x - 4 + 5x\). The correct combination should be \(2x + 5x - 4\), which results in \(7x - 4\) rather than \(10x - 4\). Therefore, the equation in Step 2 should be \(7x - 4 = 24\).

Given this analysis, the correct response is:

Step 2: The student should have added \(2x + 5x = 7x\), not \((2x)(5) = 10x\).