## Solving Equations: A Step-by-Step Guide

Solving equations is a fundamental skill in mathematics. Whether you're dealing with simple linear equations or more complex quadratic equations, understanding the process is crucial for success. This article will guide you through the process of solving equations using examples and explanations derived from user-generated content on Brainly.

### Example 1: Solving a Linear Equation

**Question:** Solve for *x*: 3x + 5 = 14

**Brainly Answer:**

- Subtract 5 from both sides: 3x + 5 - 5 = 14 - 5
- Simplify: 3x = 9
- Divide both sides by 3: 3x/3 = 9/3
- Simplify: x = 3

**Explanation:**

The goal is to isolate the variable *x* on one side of the equation. We achieve this by performing inverse operations on both sides.

**Subtracting 5 from both sides:**This eliminates the constant term (+5) on the left side.**Dividing both sides by 3:**This isolates*x*by eliminating the coefficient (3) in front of it.

**Additional Tip:** Always check your solution by substituting the value of *x* back into the original equation. In this case, 3(3) + 5 = 9 + 5 = 14, confirming that x = 3 is the correct solution.

### Example 2: Solving a Quadratic Equation

**Question:** Solve for *x*: x² - 4x + 3 = 0

**Brainly Answer:**

- Factor the quadratic expression: (x - 1)(x - 3) = 0
- Set each factor equal to zero: x - 1 = 0 or x - 3 = 0
- Solve for
*x*: x = 1 or x = 3

**Explanation:**

Quadratic equations are equations with a term containing *x²*. They can be solved by factoring, completing the square, or using the quadratic formula. Here, factoring is used:

**Factoring:**We find two numbers that multiply to 3 and add up to -4 (the coefficients of the*x²*and*x*terms, respectively). These numbers are -1 and -3.**Setting factors to zero:**Since the product of two factors is zero, at least one of them must be zero.**Solving for**We solve each simple linear equation to find the two solutions.*x*:

**Additional Tip:** Not all quadratic equations can be easily factored. In such cases, using the quadratic formula is a more general approach. The quadratic formula solves for *x* in the equation ax² + bx + c = 0 and is given by:

x = (-b ± √(b² - 4ac)) / 2a

### Conclusion

Solving equations requires understanding the basic principles of inverse operations and algebraic manipulations. While Brainly provides valuable insights and step-by-step solutions, it's crucial to understand the underlying concepts and practice solving different types of equations to gain confidence. Remember to check your solutions and explore different methods for solving equations to broaden your mathematical skills.