Question

Write and solve the equation and then check your answer.

Four times a number is thirty-two.

Which statements are true? Select the three that apply.

(3 points)
Responses

This is a multiplication problem.
This is a multiplication problem.

To solve the equation, multiply both sides by 4.
To solve the equation, multiply both sides by 4.

The correct equation is m4=32
.
The correct equation is m over 4 is equal to 32.

This is a division problem.
This is a division problem.

To solve the equation, divide both sides by 4.
To solve the equation, divide both sides by 4.

The correct equation is 4m=32
.

Answer 1

To translate the phrase "Four times a number is thirty-two" into an equation, we can define the unknown number as \( m \). The phrase can be represented as:

\[ 4m = 32 \]

Now, let's solve the equation:

1. Divide both sides of the equation by 4 to isolate \( m \):
\[
m = \frac{32}{4}
\]
2. This simplifies to:
\[
m = 8
\]

Next, we check the solution by substituting \( m = 8 \) back into the original context of the problem:

Four times the number \( 8 \):
\[
4 \times 8 = 32
\]

Since this statement is true, the solution is verified.

Now, let's evaluate the statements given:

1. **This is a multiplication problem.** - **True** (because it involves multiplying a number by 4).
2. **To solve the equation, multiply both sides by 4.** - **False** (we actually divide both sides by 4).
3. **The correct equation is \( m4=32 \).** - **False** (the correct equation should be written as \( 4m = 32 \)).
4. **The correct equation is \( m \) over 4 is equal to 32.** - **False** (this would imply \(\frac{m}{4} = 32\), which is incorrect).
5. **This is a division problem.** - **False** (the setup involves multiplication; however, the method of solving involves division).
6. **To solve the equation, divide both sides by 4.** - **True** (we divide by 4 to isolate \( m \)).
7. **The correct equation is \( 4m=32 \).** - **True** (this is the correct representation of the problem).

So, the three true statements are:
1. This is a multiplication problem.
2. To solve the equation, divide both sides by 4.
3. The correct equation is \( 4m=32 \).