How to Solve Linear Equations: A Step-by-Step Guide

Linear equations are essential to algebra and have practical applications in various fields. Learning how to solve linear equations is a fundamental skill that is important for success in math and beyond. In this step-by-step guide, we will cover the process for solving linear equations.

Step 1: Simplify the equation The first step in solving a linear equation is to simplify it by combining like terms. To do this, use the distributive property and the rules of addition and subtraction. For example, let's consider this equation:

3x + 2 - 5x = 4x - 6

Combine the x terms on one side and the constants on the other side, by subtracting 2 and 4x from each side:

3x - 5x - 4x = - 6 - 2

Simplify the equation to get:

-6x = -8

Step 2: Isolate the variable The second step is to isolate the variable on one side of the equation. To do this, use the rules of multiplication and division. In the example above, we can isolate x by dividing both sides of the equation by -6:

-6x/-6 = -8/-6

x = 4/3

Step 3: Check your answer The final step is to check your answer by plugging it back into the original equation. If the equation is true, then the answer is correct. If the equation is false, then the answer is incorrect. Let's check our answer from the example above:

3x + 2 - 5x = 4x - 6

3(4/3) + 2 - 5(4/3) = 4(4/3) - 6

4 + 2 - 20/3 = 16/3 - 6

-2/3 = -2/3

Since the equation is true, our answer is correct!
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Conclusion: Solving linear equations is a fundamental skill that has practical applications in various fields. By following these steps, you can confidently solve linear equations and apply this skill to real-world problems. Learning how to solve linear equations is an important step in your journey towards success in math and beyond.

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