Determining the Value of X in an Algebraic Equation: A Comprehensive Guide

Algebra is a fundamental part of mathematics, and understanding how to solve equations is a crucial skill. In this article, we will explore the process of determining the value of x in an algebraic equation, using a specific example to illustrate the steps involved. By the end of this guide, you will have a clear understanding of how to approach similar problems and the importance of accurate calculations.

Solving the Equation 3x – y 18 when y 27

Let's start with a straightforward example: solving the equation 3x – y 18 when y 27.

First, we substitute the given value of y into the equation: 3x – 27 18 Next, we isolate the term with x by adding 27 to both sides of the equation: 3x – 27 27 18 27 Perform the addition on both sides: 3x 45 Finally, we solve for x by dividing both sides by 3: 3x / 3 45 / 3 This simplifies to: x 15

Given the multiple-choice options in the question, none of them are correct. Therefore, the correct value of x is 15.

Additional Examples for Practice

To further illustrate the process, let's consider a couple more examples to help solidify your understanding.

Example 1

Consider the equation 3x - y 18, with y 27.

Substitute y 27 into the equation: 3x - 27 18 Add 27 to both sides: 3x 45 Divide both sides by 3: x 15

Example 2

Now, let's solve another equation: 3x - y 18 when y 54.

Substitute y 54 into the equation: 3x - 54 18 Add 54 to both sides: 3x 72 Divide both sides by 3: x 24

Conclusion

Mastering algebraic equations is essential for advancing in mathematical studies. By following the steps outlined in this article, you can confidently solve a wide range of problems. Remember to carefully substitute the given values, isolate the variable, and simplify your solutions. If you encounter any difficulties or have questions, don’t hesitate to seek additional resources or help from a tutor.

Related Keywords

Keyword 1: algebraic equations

Understanding and solving algebraic equations form the foundation of more advanced mathematical concepts. Algebraic equations are expressions that represent various mathematical relationships and are used in countless real-world applications, from economics to physics.

Keyword 2: solving equations

Solving equations is a critical skill in mathematics. This involves finding the unknown values that satisfy the given equation. Techniques for solving equations include isolating the variable, using inverse operations, and checking for extraneous solutions.

Keyword 3: value of x

In algebra, the value of x is often a mystery that needs to be solved. Finding the value of x not only helps in understanding the equation itself but also in applying it to solve more complex problems.