## Introduction to Linear Equations

Linear equations are fundamental components of algebra that you frequently encounter in mathematics. A linear equation is an equation that forms a straight line when graphed. It typically looks like *ax + b = c*, where *a*, *b*, and *c* are constants, and *x* is the variable. In this article, we’ll focus on solving linear equations that have variables on both sides.

## Understanding the Concept

To grasp the idea of solving linear equations with variables on both sides, consider the equation:

Our goal is to find the value of *x* that makes this equation true. To do this, we’ll need to isolate the variable *x* on one side of the equation.

## Steps for Solving the Equation

Let’s break down the steps to solve the equation :

**Move the variable terms to one side.**Subtract from both sides to get:Which simplifies to:

**Isolate**Subtract 4 from both sides to get:*x*by moving the constant terms to the other side.Which simplifies to:

**Verify your solution.**Plug back into the original equation to ensure both sides are equal:Since both sides are equal, the solution is correct.

## Common Mistakes and How to Avoid Them

When solving linear equations with variables on both sides, students often make mistakes. Here are common errors and tips to avoid them:

*Forgetting to move all terms involving the variable to one side.*Always move all*x*terms to one side first before simplifying.*Failing to perform equal operations on both sides.*Whatever operation you perform on one side, do it on the other side to maintain the equation’s balance.*Overlooking the verification step.*It’s crucial to substitute your answer back into the original equation to verify its correctness.

## Practice Problems

To strengthen your understanding, try solving these practice problems:

Keep practicing, and you’ll be a master at solving linear equations with variables on both sides in no time!