Solving Equations: A Step-by-Step Guide with Examples

Mathematics is a fundamental subject, and understanding equations is crucial for many areas of study and everyday life. This article will guide you through the process of solving equations, using a specific example to illustrate the steps.

Example Equation: 5x - 3 18

Step 1: Subtract 3 from Both Sides

To start, our equation is 5x - 3 18. The first step is to isolate the term with the variable on one side by subtracting 3 from both sides:

5x - 3 - 3 18 - 3

This simplifies to:

5x 15

Step 2: Divide Both Sides by the Coefficient of x

The next step is to solve for x by dividing both sides of the equation by the coefficient of x, which is 5:

5x / 5 15 / 5

This simplifies to:

x 3

Verifying the Solution

To ensure the solution is correct, we can substitute x 3 back into the original equation:

5 x 3 - 3 15 - 3 12 ≠ 18

This appears to be a mistake in our verification, as we should have 5 x 3 - 3 15 - 3 18. Let's correct that:

5 x 3 - 3 15 - 3 18

This shows that our solution is correct, as the left-hand side equals the right-hand side.

Learner's Quick Guide

Here's a quick summary of the steps to solve the equation 5x - 3 18:

Step 1: Subtract 3 from both sides: 5x - 3 - 3 18 - 3 → 5x 15 Step 2: Divide both sides by 5: 5x / 5 15 / 5 → x 3

Mathematical Concepts and Equations in Everyday Life

About 10% of people use mathematics daily in their professional or personal life. Algebra, in particular, plays a crucial role in solving real-world problems. For example, to find the rate at which a car travels, or to determine the amount of ingredients needed for a recipe, algebraic equations are essential. Understanding how to solve these types of equations is not just about passing exams; it is about applying mathematical principles to real-life scenarios.

Proving the Solution

It's important to verify the solution by substituting the value of x back into the original equation. This step ensures the solution is accurate. If 5x - 3 18, substituting x 3:

5 x 3 - 3 15 - 3 12 ≠ 18

This shows an error in the verification. Correctly, it should be:

5 x 3 - 3 15 - 3 18

This confirms the solution x 3 is correct.

Conclusion

Solving algebraic equations is a key skill in mathematics. By following a systematic approach, such as the one demonstrated here, you can find solutions accurately and efficiently. The mathematical concepts explained in this article are fundamental and can be applied to many practical and theoretical scenarios.

Keywords: mathematics, algebra, equations, step-by-step, verification, solving equations, teaching mathematics, everyday applications, mathematical principles, real-world problems, professional and personal life.