Solving Linear Equations: A Comprehensive Guide with Example on (x - 3/5 - 2 2x/5)
Understanding Linear Equations
Linear equations are fundamental in algebra and form the basis for more complex mathematical problems. They are essential for various real-world applications, such as budgeting, economics, and engineering. This article explores the process of solving linear equations through a detailed example: x - 3/5 - 2 2x/5.
Step-by-Step Guide to Solving the Given Equation
1. Start with the Equation
The given equation is:
[ x - frac{3}{5} - 2 frac{2x}{5} ]
2. Simplify the Equation
To eliminate the fraction, we can multiply every term by 5 (the denominator of the fraction). This simplifies the equation and makes it easier to solve. Here's how:
5 * (x - 3/5 - 2) 5 * (2x/5)
3. Distribute and Simplify
Lets distribute the 5 and simplify the terms:
[ 5x - 5 * frac{3}{5} - 5 * 2 2x ]
[ 5x - 3 - 10 2x ]
[ 5x - 13 2x ]
4. Combine Like Terms
Next, we need to isolate the variable on one side of the equation. To do this, we move all terms containing the variable to one side and all the remaining terms to the other side:
[ 5x - 2x 13 ]
[ 3x 13 ]
5. Solve for x
To find the value of (x), we divide both sides by 3:
[ x frac{13}{3} ]
[ x -13 ]
Conclusion
The final solution to the equation ( x - frac{3}{5} - 2 frac{2x}{5} ) is ( x -13 ).