Solving the Equation 3x - 15 2: Step-by-Step Guide

Algebra is a fundamental part of mathematics, and solving linear equations is a common task that forms the basis of many more complex mathematical problems. In this article, we will walk through the steps required to solve the equation 3x - 15 2.

Understanding the Problem

Our given equation is 3x - 15 2. This is a linear equation in one variable, where x is the variable we need to determine. The equation is straightforward and can be solved through a series of algebraic operations.

Step-by-Step Solution

Distribute the 3

The first step is to distribute the 3 across the term (x - 5). This is done by multiplying 3 by each term inside the parenthesis:

3(x - 5) 3x - 15

3x - 15 2

Combine Like Terms

The next step is to combine the like terms on the left side of the equation. Here, the only like terms are the constant terms:

3x - 15 15 2 15

Thus, we get:

3x 17, but this isn't necessary for continuing with the given problem. Instead:

3x - 35 2 directly simplifies to 3x - 35 35 2 35

Resulting in: 3x 37, but again, not needed for this problem. We will focus on the simplification and solution provided.

Subtract 2 from Both Sides

To isolate the term with the variable, subtract 2 from both sides of the equation:

3x - 35 - 2 2 - 2

Which simplifies to:

3x - 35 0

Divide Both Sides by 3

To solve for x, divide both sides of the equation by 3:

3x/3 0/3

This simplifies to:

x 0

Conclusion

Through these steps, we have determined that the solution to the equation 3x - 15 2 is x 0.

Understanding each step in solving linear equations is crucial for more advanced mathematical topics. If you're new to algebra, practice is key! You can try applying these steps to similar equations to build your confidence.