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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.

3 answers

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:

\[ 2x + 14 = 3x \]

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

\[ 14 = 3x - 2x \]

This simplifies to:

\[ 14 = x \]

  1. 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:

\[ \boxed{14} \]

can you make it less advanced

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: \[ \boxed{14} \]