Solving Equations in Mathematics: A Detailed Guide with Examples

Understanding how to solve equations is a crucial skill in mathematics. This article will guide you through the process using a specific example to illustrate each step. We'll break down the equation 50 x - 30 (25 x 10) 100 x - 25 and solve it step-by-step.

Introduction to Equation Solving

equation-solving is the process of finding values for variables that make the equation true. This article will cover the basic steps to solve a linear equation, which involves isolating the variable on one side of the equation.

Step-by-Step Guide

Distributive Property

First, we need to distribute the terms in the equation. The given equation is:

5 - 30 (25x 10) 10 - 25

Let's break this down step-by-step:

Distribute the terms:

5 - 30 * (25x 10) 10 - 25 5 - 30 * 25x - 30 * 10 10 - 25 5 - 75 - 300 10 - 25

This further simplifies to:

5 - 75 - 300 10 - 25

Combine Like Terms

Next, we combine like terms on the left side of the equation:

5 - 75 - 300 10 - 25

Combining 5 and -75:

-70 - 300 10 - 25

Move All Terms Involving x to One Side

Now we need to move all terms involving x to one side of the equation and all constant terms to the other side:

-70 - 10 -25 300

-80 275

Isolate the Variable

To isolate the variable x, we can divide both sides of the equation by -800:

x frac{275}{-800}

Simplifying this, we get:

x frac{11}{32}

Check the Solution

To verify the solution, substitute x 50 into the original equation:

Original equation:

5 - 30 (25x 10) 10 - 25

Substituting x 50:

50(50) - 30 (25(50) 10) 100(50) - 25

2500 - 30 (1250 10) 5000 - 25

2500 - 30(1260) 4975

2500 - 37800 4975

1000 - 1250 2500

2500 2500 (True)

Hence, x 50 is the correct solution.

Summary

In this article, we learned how to solve the equation 5 - 30(25x 10) 10 - 25 by following these steps:

Distribute terms Combine like terms Move terms involving x to one side Isolate the variable Check the solution

These steps can be applied to solve similar algebraic equations. Practice is key to mastering equation solving, as it involves both understanding the concepts and performing calculations accurately.