Solving Equations with Variables: A Guide to Basic Algebra

Welcome to our comprehensive guide on solving equations with variables, where we will walk you through the process with detailed examples. Understanding how to solve basic algebraic equations is crucial for many fields, including mathematics, engineering, and data science. In this article, we'll focus on a specific example that many students encounter in their early algebra classes:

Example Problem: x 2.7 7.2 - 2.7

Let's break down the process step-by-step, ensuring clarity and accessibility for readers of all levels. We'll provide explanations, additional examples, and tips to help you master similar problems. By the end, you'll have a solid grasp of how to approach these types of equations.

Step-by-Step Solution

The given equation is:

x 2.7 7.2 - 2.7

First, let's simplify the right-hand side of the equation:

Subtract 2.7 from 7.2:

7.2 - 2.7 4.5

So, the equation becomes:

x 2.7 4.5

Our goal is to solve for x. This means we need to isolate x on one side of the equation. To do this, we'll need to divide both sides of the equation by 2.7:

x 4.5 / 2.7

Perform the division:

4.5 / 2.7 ≈ 1.66666666667

Simplify the result:

x ≈ 1.67 (rounded to two decimal places)

Understanding the Solution

In the end, we find that x ≈ 1.67. This means that when we multiply 1.67 by 2.7, we get approximately 4.5, which matches the right-hand side of our original equation:

1.67 * 2.7 4.5

Additional Examples

To help solidify your understanding, let's look at a few more examples:

Example 1: 3x 12

3x 12

Divide both sides by 3:

x 12 / 3 4

Example 2: 0.5x 2.5

0.5x 2.5

Divide both sides by 0.5:

x 2.5 / 0.5 5

Tips and Tricks

Here are some tips to help you solve similar equations more efficiently:

Always simplify the right-hand side before proceeding to isolate the variable. Remember to perform the same operation on both sides of the equation to maintain balance. Use estimation or simplification techniques to verify your results, ensuring accuracy.

Conclusion

Solving equations with variables is a fundamental skill in algebra. By following the steps outlined in this guide, you can solve a variety of equations with ease. Whether you're a student or a professional in a related field, mastering algebra will open doors to a wealth of knowledge and opportunities.

Feel free to explore more algebraic problems and challenge yourself. With practice and persistence, you'll become proficient in solving even more complex equations.