To explain how \( x = 75 \) was obtained, I'll need more context about the problem. There are various ways this result could have been derived, depending on the type of equation or mathematical problem you were working on. 

Here are some common scenarios:

1. **Linear Equation**: If you were solving a linear equation like \( 2x + 25 = 175 \), you would subtract 25 from both sides, getting \( 2x = 150 \), and then divide both sides by 2 to find \( x = 75 \).

2. **Quadratic Equation**: In a quadratic equation like \( x^2 - 150x + 5625 = 0 \), you might factor it as \( (x - 75)(x - 75) = 0 \), leading to \( x = 75 \).

3. **Proportion**: If you had a proportion like \( \frac{x}{100} = \frac{3}{4} \), you would multiply both sides by 100, giving \( x = 75 \).

4. **Inequality**: If solving an inequality \( x - 50 \geq 25 \), adding 50 to both sides would give \( x \geq 75 \).

5. **Geometric Interpretation**: If the problem involved a geometric figure, such as a triangle with one angle measuring \( x \) and the other angles being 45° and 60°, you could find that \( x = 180° - 45° - 60° = 75° \).

6. **Arithmetic Mean**: If you had a set of numbers like \( 70, 75, 80 \), you might calculate the arithmetic mean \( \frac{70 + 75 + 80}{3} = 75 \).

7. **Percentage Problem**: In a percentage problem, you might be asked what number is 75% of 100, which directly gives \( x = 75 \).

8. **Simplified Ratio**: If you have a ratio such as \( \frac{x}{25} = 3 \), multiplying both sides by 25 yields \( x = 75 \).

Please provide more details about the problem, and I can give a specific explanation. 

Would you like more details on any of these methods, or do you have a particular equation in mind?

### Relative Questions:
1. How do you solve a linear equation step by step?
2. What are the methods for solving a quadratic equation?
3. How do you handle inequalities when solving for a variable?
4. What is the process of solving a proportion equation?
5. How is the arithmetic mean calculated from a set of numbers?
6. What strategies are used to solve percentage problems?
7. How can ratios be simplified and used to find unknown values?
8. How do you find the angles in a geometric shape, such as a triangle?

### Tip:
When solving equations, always perform the same operation on both sides to maintain equality.

Understand how the result x = 75 was obtained through detailed explanations and examples. Explore methods such as solving linear equations, quadratic equations, proportions, inequalities, geometric interpretations, arithmetic means, percentage problems, and ratio simplifications.

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