One method for solving 3(x−4)=18

Question

is to first divide by 3, then add 4. Which method below would also result in the correct answer?(1 point)
Responses.

First, distribute the 3, then add 4, and lastly divide by 3.
First, distribute the 3, then add 4, and lastly divide by 3.

First, multiply by 13
, then subtract 4.
First, multiply by Start Fraction 1 over 3 End Fraction , then subtract 4.

First, distribute the 3, then add 12, and lastly divide by 3.
First, distribute the 3, then add 12, and lastly divide by 3.

First, divide by 3, then subtract 4.
First, divide by 3, then subtract 4.

Answer 1

To solve the equation \( 3(x - 4) = 18 \), let's analyze the suggested methods.

1. First, distribute the 3, then add 4, and lastly divide by 3.

   • Distributing gives \( 3x - 12 = 18 \).
   • Adding 12 gives \( 3x = 30 \).
   • Dividing by 3 gives \( x = 10 \). This method is correct.

2. First, multiply by \( 13 \), then subtract 4.

   • This approach does not make sense in the context of solving the equation correctly. This method is not correct.

3. First, multiply by \( \frac{1}{3} \), then subtract 4.

   • Multiplying by \( \frac{1}{3} \) gives \( x - 4 = 6 \).
   • Subtracting 4 gives \( x = 10 \). This method is correct.

4. First, distribute the 3, then add 12, and lastly divide by 3.

   • This yields the same step as the first one: you add 12 after distributing \( 3x - 12 = 18 \), giving \( 3x = 30 \) and then dividing gives \( x = 10 \). This method is correct.

5. First, divide by 3, then subtract 4.

   • Dividing gives \( x - 4 = 6 \) and subtracting 4 is incorrect since no addition has occurred prior to that step. It will lead to an incorrect operation. This method is not correct.

So, the methods that will result in the correct answer are:

1. First, distribute the 3, then add 4, and lastly divide by 3.
2. First, multiply by \( \frac{1}{3} \), then subtract 4.
3. First, distribute the 3, then add 12, and lastly divide by 3.

Therefore, any of these three methods (the first, the third, and the second) will result in the correct answer. However, among the options you're given, the first and third methods are the most clearly aligned with the original choices you provided.

Answer 2

pick one

Answer 3

I would choose:

First, distribute the 3, then add 12, and lastly divide by 3.

This method will correctly lead to the solution for the equation \(3(x - 4) = 18\).

Answer 4

When solving the equation −12(x+10)=−3
, identify the operation that should be done first.(1 point)
Responses

multiply by −2
multiply by negative 2

subtract 10
subtract 10

add 10
add 10

divide by −2

Answer 5

To solve the equation \( -12(x + 10) = -3 \), the first operation you should perform is to divide by -12 to isolate the term \((x + 10)\).

However, that option is not present in your responses. Let's analyze the given options:

1. Multiply by -2: This does not help to isolate \(x\) directly.
2. Subtract 10: This does not simplify the equation effectively at this stage.
3. Add 10: This is not the first operation you would perform based on the layout of the equation.
4. Divide by -2: This is also not applicable since you are working with -12.

Given these options, none of them are the correct first step to solve the equation \( -12(x + 10) = -3 \).

However, if we refer to the closest choice in context and considering how you might simplify the equation towards isolating \(x\), the option to divide by -12 (though not given) is ideal. From your provided options, the best next step after any simplification would usually be done through dividing the entire equation (eventually) but the question specifically asks what should be done first.

Based on the nature of your exact question, if forced to select one of the options just for the sake of completion here without the notion of using -12:

Since none of the answers are directly usable to isolate \(x\) immediately, in pure arithmetic simplification, you would practically lean towards dividing (by whatever necessary), but that isn't listed here.

Under realistic tasks and contexts, refer back to dividing out -12 being ideal but from your options perhaps clarify how they relate; otherwise, the logical first operation isn't listed cleanly here based on pure mathematical steps.

Answer 6

When solving the equation −1/2(x+10)=−3
, identify the operation that should be done first.(1 point)
Responses

multiply by −2
multiply by negative 2

subtract 10
subtract 10

add 10
add 10

divide by −2

Answer 7

To solve the equation \( -\frac{1}{2}(x + 10) = -3 \), the best first operation is to eliminate the fraction by multiplying both sides by \(-2\).

Let's analyze the options:

1. Multiply by -2: This is the correct first operation. It will eliminate the \(-\frac{1}{2}\) in front of the parenthesis.

   \[ -2 \cdot -\frac{1}{2}(x + 10) = -2 \cdot -3 \implies x + 10 = 6 \]

2. Subtract 10: This would not be appropriate as the first operation since you won't have isolated \(x\) yet.

3. Add 10: This is not the correct initial operation for solving the equation.

4. Divide by -2: This would result in the same outcome as multiplying by -2, but it does not directly address the fraction.

Therefore, the first operation that should be done is:

Multiply by -2.

Answer 8

Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket. (1 point)
Responses

Add 3 to 75.
Add 3 to 75.

Subtract 6 from 75.
Subtract 6 from 75.

Divide 75 by 3.
Divide 75 by 3.

Divide 75 by 6.
Divide 75 by 6.
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Answer 9

To solve the problem, let's define the variables first:

• Let \( A \) be the cost of one adult ticket.
• Let \( C \) be the cost of one child ticket.

According to the problem:

1. The total cost of three adult tickets and three child tickets is $75: \[ 3A + 3C = 75 \]

2. The cost of each child ticket is $3 less than the cost of an adult ticket: \[ C = A - 3 \]

To find \( A \) and \( C \), the first step in solving the equations is to simplify the equation \( 3A + 3C = 75 \).

From this equation, you can divide all terms by 3 to simplify:

\[ A + C = 25 \]

Now, substitute \( C = A - 3 \) into this simplified equation:

\[ A + (A - 3) = 25 \]

Combine and solve:

\[ 2A - 3 = 25 \]

So, the first correct arithmetic step to solve this problem is:

Divide 75 by 3.

This leads to the equation \( A + C = 25 \), which will help you find the costs of both tickets.

Answer 10

Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. The first step to solving this problem algebraically is to write an equation: 3(x+x−3)=75
, where x
represents the cost of an adult ticket. Identify the next step, which would simplify the equation before solving for the variable. (1 point)
Responses

Divide 75 by 3.
Divide 75 by 3.

Distribute values over the variables.
Distribute values over the variables.

Combine like terms in parentheses.
Combine like terms in parentheses.

Add 3 to 75
Add 3 to 75
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Answer 11

Let's first rewrite the equation you provided for clarity:

The equation based on the problem statement is:

\[ 3(x + (x - 3)) = 75 \]

Where \( x \) represents the cost of an adult ticket.

From here, the next logical step to simplify the equation before solving for the variable \( x \) would be to distribute values over the variables.

Here’s how you proceed:

1. Distribute the 3 across the terms inside the parentheses:

\[ 3(x + (x - 3)) = 75 \]

becomes

\[ 3x + 3(x - 3) = 75 \]

2. This will simplify to:

\[ 3x + 3x - 9 = 75 \]

So, the correct choice from your given options is:

Distribute values over the variables.