Solving 3x36 by Factoring: A Comprehensive Guide
Algebra is the cornerstone of many advanced mathematical concepts, and one of the fundamental skills in algebra is factoring. In this article, we will explore how to solve 3x36 by factoring, a common approach to linear equations. This guide will provide step-by-step instructions and practical examples to help you master this technique. By the end of this article, you will be able to confidently solve similar problems on your own.
Understanding the Problem: 3x36
The equation 3x36 can be understood as a linear equation where we need to solve for x. The goal is to find the value of x that satisfies the equation.
Method 1: Factoring by Setting the Equation to Zero
One common approach to solving linear equations is to set the equation to zero. This method involves moving all terms to one side of the equation so that the other side is zero.
Start with the equation: 3x36. This can be simplified to 3x - 36 0.
Isolate the term involving x: To do this, we need to move the constant term, -36, to the other side of the equation. Add 36 to both sides of the equation. This gives us:
3x - 36 36 0 36
3x 36
Solve for x: Now, divide both sides of the equation by 3 to isolate x.
3x / 3 36 / 3
x 12
Method 2: Factoring by Direct Factorization
Factoring involves writing an equation as a product of two or more expressions. For the equation 3x36, we can directly factor it by examining the constants involved.
Identify the constants: In the equation 3x - 36, the constants are 3 and 36.
Find a common factor: Look for a common factor between the coefficient of x (which is 3) and the constant (-36). Both 3 and -36 are divisible by 3.
Factor out the greatest common factor (GCF): Factor out 3 from the equation.
3(x - 12) 0
Set each factor equal to zero: Since the product of the factors is zero, one of the factors must be zero.
x - 12 0
x 12
Conclusion and Further Practice
By using either method, we arrive at the same solution: x 12. This confirms that the value of x that satisfies the equation 3x36 is 12.
To further enhance your understanding and skills, it is recommended to practice similar problems. Solving a variety of linear equations through factoring will solidify your knowledge and make you more proficient in algebra. Additionally, exploring other types of equations and their solutions can expand your mathematical toolkit.
Happy math solving!