the sum of twice a number and 7 is the difference between the number and 2

Let's translate the problem into an equation:

Let the unknown number be \( x \).

- "Twice a number" translates to \( 2x \).
- "The sum of twice a number and 7" translates to \( 2x + 7 \).
- "The difference between the number and 2" translates to \( x - 2 \).

The equation based on the problem statement is:

\[
2x + 7 = x - 2
\]

Now, let's solve the equation:

1. Subtract \( x \) from both sides to get the terms involving \( x \) on one side:

\[
2x - x + 7 = x - x - 2
\]

Simplifying:

\[
x + 7 = -2
\]

2. Subtract 7 from both sides to isolate \( x \):

\[
x = -2 - 7
\]

Simplifying:

\[
x = -9
\]

The solution is \( x = -9 \).

Would you like a detailed breakdown or have any questions?

Here are 5 related questions:
1. What would the equation be if the sum was the product instead?
2. How would the problem change if the 7 were replaced by another number?
3. What is the solution if the sum of three times the number and 5 is the difference between the number and 3?
4. How can we represent the problem graphically?
5. What if the problem involved the square of the number instead of twice the number?

**Tip:** When solving equations, always aim to simplify the equation step by step, making sure to keep the equation balanced by performing the same operation on both sides.

Learn how to solve the equation where twice a number plus 7 equals the difference between the number and 2. This problem involves translating verbal statements into algebraic equations and solving them step-by-step. Suitable for students in Grades 7-9.

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