Solving Equations: Unlocking the Value of 'x' in Mathematical Expressions

Mathematics is the backbone of various fields, from engineering to economics, and understanding how to solve equations is a fundamental skill. This guide aims to walk you through solving a specific equation to determine the value of x. Whether you're a student looking to enhance your mathematical skills or a professional needing to strengthen your analytical capabilities, this article will provide a clear, step-by-step explanation.

Discover how to tackle this fundamental algebra problem and similar ones with confidence.

Understanding the Equation

Let's first look at the equation: 15x 7 3 - 172. This is a linear equation in one variable. Linear equations are equations where the highest power of the variable is 1. They usually take the form Ax B C, where A, B, and C are constants and x is the variable we solve for.

Step-by-Step Solution

The goal is to isolate x on one side of the equation. Let's walk through the steps in detail:

Combine like terms: In the equation 15x 7 3 - 172, the 7 and -172 on the right-hand side (RHS) are like terms. Combine them to simplify the equation. Isolate x: To isolate x, we need to move all terms with x to one side and all constant terms to the other side. Shifting the 15x to the RHS and the 172 to the LHS gives us a clearer view of the variables and constants. Perform the calculation: After shifting the terms, solve the equation to find the value of x.

Let's represent these steps mathematically:

Combine the constants:

7 - 172 3 - 15x

Move the x-term to the RHS:

7 - 172 3 - 15x

Shifting 15x to RHS and 172 to LHS:

15x 3 - 172 7

Simplifying the right-hand side:

15x -162

Solve for x:

x -162 / 15

Dividing both sides by 15:

x -10.8

The value of x in the equation 15x 7 3 - 172 is -10.8.

Application of Linear Equations

While solving individual equations is a crucial skill, understanding their underlying principles can help in more complex areas of mathematics and everyday life. Linear equations are used in fields such as:

Physics: for modeling motion, energy, and velocity. Economics: to analyze supply and demand in markets. Finance: for calculating interest rates and investment returns. Engineering: for calculating stress and strain in materials. Data Science and Machine Learning: for fitting models and making predictions.

By mastering the techniques of solving linear equations, you'll be better equipped to handle advanced mathematical concepts and real-world problems.

Conclusion

Solving the equation 15x 7 3 - 172 demonstrates the fundamental skills required to manipulate and solve algebraic equations. Understanding these steps can be invaluable in various fields and personal endeavors. Practice solving similar equations to build your confidence and proficiency in algebra.