Solving Advanced Algebraic Equations: A Step-by-Step Guide

Dealing with complex algebraic equations can be daunting, but with a systematic approach, solving problems like 3x-2/10-x3/74x-7/3x-1 becomes much more manageable. This guide walks you through the process, providing a detailed solution and highlighting key steps to successfully solve any advanced equation.

1. Group Common Values

To simplify the given equation, the first step is to group common values. In the equation 3x-2/10-x3/74x-7/3x-1, we can combine the terms involving x and the constant terms:

6x - 2/10 - 3/7 - 4x - 7/3 x - 1

2. Bring 1 Over and Move All Xs to the Right

The next step is to bring the constant 1 from the left side of the equation to the right side. This means we need to move all terms containing the variable x to the right side of the equation:

-2/10 - 3/7 - 4x - 7/3 x - 1 - 1

-2/10 - 3/7 - 4x - 7/3 x - 2

3. Find Common Denominators

For the equation to be solvable, we need to find a common denominator for the fractions. Here, we find the least common multiple (LCM) of the denominators 10, 7, and 3:

-42/210 - 90/210 - 4(210)/210 - 7(70)/210 x - 2

-42/210 - 90/210 - 840/210 - 490/210 x - 2

-1,462/210 x - 2

4. Add Them Up

The next step is to combine the numerators over the common denominator:

-1462/210 x - 2

To isolate x, we need to add 2 to both sides of the equation:

-1462/210 2 x

Convert 2 to a fraction with the same denominator:

-1462/210 420/210 x

-1042/210 x

Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:

x -521/105

5. Divide by -5 to Isolate x

To isolate x, divide both sides by -5:

x -521/105 ÷ -5

x 1042/525

This is the final solution to the given equation, and it can be expressed as:

x 116/525

By following these steps, you can tackle complex algebraic equations with confidence. Remember, the key is to break down the problem into manageable parts and simplify your work as you go.

Additional Resources

For further practice and understanding, consider exploring additional resources like:

Khan Academy’s Algebra Solving Linear Equations Math is Fun’s Systems of Linear Equations ’s Algebra Solver

By visiting these resources, you can deepen your knowledge and improve your skills in solving algebraic equations.