## Introduction to Linear Equations

A linear equation is a type of equation where the highest power of the variable is one. It’s called “linear” because it represents a straight line when graphed on a coordinate plane. The general form of a linear equation is:

Where is the coefficient, is the constant, and is the variable. Solving these equations is a fundamental skill in algebra that lays the groundwork for more complex mathematical concepts. Let’s explore how to solve linear equations with the variable on one side.

## Basic Principles of Solving Linear Equations

When solving linear equations, our goal is to isolate the variable on one side of the equation. Here are some fundamental principles to keep in mind:

**Addition and Subtraction:**You can add or subtract the same number from both sides of the equation without changing the equality. For example:Subtracting 3 from both sides gives:

**Multiplication and Division:**You can multiply or divide both sides of the equation by the same non-zero number without changing the equality. For example:Dividing both sides by 3 gives:

Let’s delve deeper into these principles with more examples and problems to solve.

## Step-by-Step Guide to Solving Linear Equations

Consider the equation . To solve this, we need to isolate . Here’s a step-by-step guide:

**Add 5 to both sides:**Simplifies to:

**Divide both sides by 4:**Simplifies to:

Thus, the solution to the equation is .

## Real-World Applications

Linear equations are not just abstract mathematical concepts; they can also model real-world situations. For example, consider you have 2 each day. The equation representing the number of days () after which you have

10 left.

## Practice Problems

To solidify your understanding, here are some practice problems. Try to solve them on your own:

- Solve .
- Solve .
- Solve .

Remember to follow the principles we’ve discussed to isolate the variable and find the solution.

## Conclusion

Solving linear equations is a foundational skill in mathematics that applies to various real-world scenarios. By mastering the techniques of addition, subtraction, multiplication, and division, you can isolate the variable and solve for its value. Keep practicing, and you’ll become proficient in solving linear equations with the variable on one side.

For further reading and practice problems, refer to textbooks and online resources that focus on algebra. Happy solving!

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