One method for solving 3(x−4)=18 is to first divide by 3, then add 4. Which method below would also result in the correct answer?(1 point)

Question

Responses

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

First, divide by 3, then subtract 4.

Answer 1

To solve the equation \(3(x - 4) = 18\), one effective method is to first divide by 3 and then add 4.

Let's consider the methods listed in your question:

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

   • Multiplying both sides by \( \frac{1}{3} \) gives \((x - 4) = 6\). Subtracting 4 would not yield the correct solution.

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

   • Distributing gives \(3x - 12 = 18\). If you add 12 to both sides, you get \(3x = 30\), and dividing by 3 gives \(x = 10\). This is valid.

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

   • Distributing gives \(3x - 12 = 18\). Adding 4 does not lead to a valid operation in solving for \(x\).

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

   • Dividing gives \(x - 4 = 6\). Subtracting 4 provides \(x = 10\), which is valid.

From these options, the second method (first distribute the 3, then add 12, and lastly divide by 3) and the fourth method (first divide by 3, then subtract 4) correctly leads to the solution. Thus, the method you are looking for that also results in the correct answer is the second option.

Answer 2

What’s the answer?

Answer 3

The correct answer is:

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

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

Answer 4

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

divide by −2
divide by negative 2

multiply by −2
multiply by negative 2

subtract 10
subtract 10

add 10

Answer 5

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

So, the correct response is:

multiply by −2 (or multiply by negative 2, as both are equivalent).

This will give you:

\[ x + 10 = 6 \]

Then, you can proceed with solving for \(x\).

Answer 6

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

Divide 75 by 6.
Divide 75 by 6.

Divide 75 by 3.
Divide 75 by 3.

Subtract 6 from 75.
Subtract 6 from 75.

Add 3 to 75.

Answer 7

To solve the problem of finding the cost of adult and child movie tickets, we can start by defining the cost of each ticket using variables.

Let's denote:

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

From the problem, we have the following information:

1. Three adult tickets and three child tickets cost $75. This can be expressed as: \[ 3A + 3C = 75 \]

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

To simplify the first equation, we can divide the entire equation by 3: \[ A + C = 25 \] This gives us a simpler equation to work with.

Now using the second equation, we substitute \(C\) in the first equation: \[ A + (A - 3) = 25 \] This simplifies to: \[ 2A - 3 = 25 \]

With this setup, we can easily solve for \(A\).

Thus, the first step in the arithmetic process that helps derive the equation to find the cost of each ticket involves simplifying the equation by dividing by 3.

So, the correct answer is:

Divide 75 by 3.

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. 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

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

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

Divide 75 by 3.
Divide 75 by 3.

Add 3 to 75

Answer 9

The equation you have written is \(3(x + (x - 3)) = 75\).

To simplify this equation before solving for the variable, the next step is to combine like terms in parentheses.

Here’s how it works:

1. Inside the parentheses, you have \(x + (x - 3)\), which simplifies to \(2x - 3\).
2. The equation then becomes \(3(2x - 3) = 75\).

Thus, the correct response is:

Combine like terms in parentheses.

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. Find the price of each ticket.(1 point)
Responses

an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $12.50 and a child ticket is $9.50

an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5

an adult ticket is $11 and a child ticket is $8
an adult ticket is $11 and a child ticket is $8

an adult ticket is $14 and a child ticket is $11

Answer 11

Let's solve the problem step by step.

1. Define Variables:

   • Let \( x \) be the cost of an adult ticket.
   • The cost of a child ticket would then be \( x - 3 \).

2. Write the Equation: From the information given: \[ 3x + 3(x - 3) = 75 \]

3. Simplify the Equation: \[ 3x + 3x - 9 = 75 \] Combining like terms gives: \[ 6x - 9 = 75 \]

4. Solve for \( x \): Add 9 to both sides: \[ 6x = 84 \] Divide by 6: \[ x = 14 \]

So, the cost of an adult ticket is $14.

5. Find the Price of the Child Ticket: The cost of a child ticket: \[ x - 3 = 14 - 3 = 11 \]

Therefore, the prices are:

• An adult ticket is $14
• A child ticket is $11

The correct response is: an adult ticket is $14 and a child ticket is $11.