Question

Create an equation modeling the scenario. Use the equation to solve for the missing number. In your final answer, include the equation and all necessary calculations.

Twice the sum of a number and seven is three times the number.

Answer 1

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Answer 2

Let's denote the unknown number as \( x \).

According to the problem statement, we can model the situation with the following equation:

\[
2(x + 7) = 3x
\]

Now, let's solve for \( x \):

1. Distribute the 2 on the left side of the equation:

\[
2x + 14 = 3x
\]

2. Next, let's isolate \( x \) by subtracting \( 2x \) from both sides:

\[
14 = 3x - 2x
\]

This simplifies to:

\[
14 = x
\]

3. Therefore, the value of the unknown number \( x \) is:

\[
x = 14
\]

In summary, the equation we created was:

\[
2(x + 7) = 3x
\]

After solving, we found that the missing number is:

\[
\boxed{14}
\]

Answer 3

Sure! Let’s break it down into simpler steps.

1. **Define the number**: Let's call the unknown number \( x \).

2. **Set up the equation**: The problem says "Twice the sum of a number and seven is three times the number." This can be written as:
\[
2(x + 7) = 3x
\]

3. **Solve the equation step by step**:
- Start by expanding the left side:
\[
2(x + 7) = 2x + 14
\]
- Now the equation looks like this:
\[
2x + 14 = 3x
\]

4. **Get all the \( x \) terms on one side**:
- To do this, subtract \( 2x \) from both sides:
\[
14 = 3x - 2x
\]
- This simplifies to:
\[
14 = x
\]

5. **Conclusion**: The number we are looking for is:
\[
x = 14
\]

So, the final answer is:
\[
\boxed{14}
\]