Set up the equation for the following word problem and solve the equation. Let x be the unknown number.

8484 times a number minus 6969 is equal to 1414 less than the number.

Let's start by translating the word problem into a mathematical equation.

### Problem Breakdown:

- "8484 times a number" can be represented as \( 8484x \).
- "minus 6969" means subtract 6969 from the expression, so we have \( 8484x - 6969 \).
- "is equal to" indicates equality, so we set the equation equal to the next part of the statement.
- "1414 less than the number" means \( x - 1414 \).

### Setting Up the Equation:
The equation based on the problem statement is:

\[
8484x - 6969 = x - 1414
\]

### Solving the Equation:

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

\[
8484x - x - 6969 = -1414
\]

2. Simplify the equation:

\[
8483x - 6969 = -1414
\]

3. Add 6969 to both sides to isolate the \( x \)-term:

\[
8483x = 5555
\]

4. Divide both sides by 8483 to solve for \( x \):

\[
x = \frac{5555}{8483}
\]

### Final Answer:

\[
x = \frac{5555}{8483} \approx 0.6547
\]

So the unknown number \( x \) is approximately **0.6547**.

Would you like more details or have any other questions?

Here are some related questions:
1. How would the equation change if the constant 6969 were instead added?
2. What if the phrase "is equal to" was replaced with "is greater than"?
3. How would you set up the equation if the problem involved two unknown numbers?
4. What if 1414 was greater than the number instead of less?
5. How does the equation change if the multiplication by 8484 was instead division?

**Tip:** Always carefully translate word problems into equations by identifying operations and relationships.

Learn how to solve the equation "8484 times a number minus 6969 equals 1414 less than the number" step-by-step with a detailed solution. This problem covers key algebraic concepts, including translating word problems into equations and solving linear equations. Suitable for students in Grades 7-9.

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