Use algebraic manipulation

Oct 13, 2025 by talynt.org 101 views

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, specifically the equation $$4w = 17.96$$. We will break down the solution step by step, explaining each concept and providing examples to help illustrate the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $$ax = b$$, where $$a$$ and $$b$$ are constants, and $$x$$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation $$4w = 17.96$$

The equation $$4w = 17.96$$ is a simple linear equation in which the variable $$w$$ is multiplied by the constant $$4$$, resulting in the value $$17.96$$. To solve for $$w$$, we need to isolate the variable on one side of the equation.

Step 1: Divide Both Sides by 4

To isolate the variable $$w$$, we need to get rid of the constant $$4$$ that is multiplied by $$w$$. We can do this by dividing both sides of the equation by $$4$$. This will cancel out the $$4$$ on the left-hand side, leaving us with the variable $$w$$.

\frac{4w}{4} = \frac{17.96}{4}

Step 2: Simplify the Equation

After dividing both sides by $$4$$, we are left with the simplified equation $$w = \frac{17.96}{4}$$. This equation can be further simplified by performing the division.

Step 3: Perform the Division

To perform the division, we can use a calculator or divide the numbers manually. The result of the division is $$w = 4.49$$.

Conclusion

In this article, we solved the linear equation $$4w = 17.96$$ by dividing both sides by $$4$$ and simplifying the equation. The final solution is $$w = 4.49$$. This example illustrates the basic steps involved in solving linear equations, including isolating the variable and simplifying the equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

Physics and Engineering: Linear equations are used to describe the motion of objects, the flow of fluids, and the behavior of electrical circuits.
Economics: Linear equations are used to model economic systems, including supply and demand curves, and to analyze the behavior of economic variables.
Computer Science: Linear equations are used in computer graphics, game development, and machine learning.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

Use algebraic manipulation: Linear equations can be solved using algebraic manipulation, including addition, subtraction, multiplication, and division.
Use graphing: Linear equations can be graphed on a coordinate plane to visualize the solution.
Use substitution: Linear equations can be solved using substitution, where one variable is expressed in terms of another variable.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

Not isolating the variable: Failing to isolate the variable on one side of the equation can lead to incorrect solutions.
Not simplifying the equation: Failing to simplify the equation can lead to incorrect solutions.
Not checking the solution: Failing to check the solution can lead to incorrect answers.

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable, simplify the equation, and check the solution to ensure accuracy. With practice and patience, you can become proficient in solving linear equations and apply them to real-world problems.