Solving the Equation: The Sum of Five Times a Number and 10 Equals 39

This article will guide you through a common algebraic problem: determining an unknown number when provided with a specific equation. Specifically, we'll explore how to solve the equation: 'the sum of five times a number and 10 is 39'

Understanding the Problem

The problem statement is as follows: 'The sum of five times a number and 10 is 39'. To denote the unknown number, we use the variable x. Our task is to find the value of x that satisfies the given equation.

Setting Up the Equation

Let's translate the problem statement into a mathematical equation. If the number is x, then:

5x 10 39

Step-by-Step Solution

1. **Subtract 10 from both sides:**

5x 10 - 10 39 - 10

5x 29

2. **Divide both sides by 5:**

x frac{29}{5}

3. **Calculate the final value of x:**

x 5.8

Conclusion

The value of the unknown number is 5.8. We can represent the final answer in a variety of ways: as an improper fraction (frac{29}{5}), as a mixed fraction (5 frac{4}{5}), or as a decimal (5.8). Regardless of the format, all these representations are equivalent.

Verification

To ensure the solution is correct, let's verify the calculations. Starting with x 5.8 in the original equation:

5x 10 39

5(5.8) 10 39

29 10 39

39 39

The equality holds true, confirming that our solution is correct.

Additional Practice

Practice is key to mastering algebraic problems. Try solving similar equations to further hone your skills:

3x 8 29 7x - 5 44 4x 18 62

With each practice session, you'll become more proficient in solving such equations.