Solving Linear Equations: A Step-by-Step Guide to d - 17 4

Understanding how to solve linear equations is a fundamental skill in algebra. This article will walk you through the process of solving the equation d - 17 4 and provide a comprehensive overview of the techniques involved in doing so. Linear equations are of the form ax b c, where a, b, and c are constants, and x is the variable. By the end of this guide, you will have a clear understanding of how to solve and interpret linear equations.

Introduction to Linear Equations

A linear equation in one variable, often denoted as d, is an equation that can be written in the form ax b 0, where a and b are constants and x is the variable. In our specific equation, d - 17 4, the coefficient a is 1, and the rest of the constants are -17 and 4.

Step-by-Step Solution of d - 17 4

To solve the equation d - 17 4, follow these steps:

Add 17 to Both Sides

The first step in solving any equation is to isolate the variable. In this case, we need to remove the -17 from the left side of the equation. To do this, we add 17 to both sides of the equation. This operation maintains the equality:

d - 17   17  4   17

Since -17 17 equates to 0 on the left side, the equation simplifies to:

d  21

Understanding the Solution

The variable d is now isolated and equal to 21. This solution means that if we substitute 21 for d in the original equation, the two sides of the equation will be equal:

21 - 17  414  4 (This step is incorrect, it should be 21 - 17  4, which is correct)

The correct simplification is 21 - 17 4, which is true. Therefore, the solution is correct.

General Approach to Solving Linear Equations

The process of solving a linear equation is based on the principle that any operation performed on one side of the equation must be performed on the other side to maintain equality. Here are the general steps to solve any linear equation:

Identify the variable you are solving for. Apply inverse operations to isolate the variable. Check your solution by substituting it back into the original equation.

Additional Tips and Resources

Solving linear equations can sometimes be challenging, especially when dealing with more complex equations. Here are some additional tips and resources that can help you:

Use BIDMAS/BODMAS/BEDMAS: This is the order of operations, which stands for Brackets, Indices/Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This principle is crucial for correctly solving and verifying your equations. Utilize Math Solvers: Use tools like Cymath Math Problem Solver with Steps for step-by-step solutions to a wide range of math problems. This can help you understand the solution process and identify any mistakes you might have made. Khan Academy: Khan Academy offers comprehensive tutorials and exercises on solving linear equations and other algebraic concepts. It is a valuable resource for both beginners and advanced learners.

Conclusion

Solving the equation d - 17 4 is a straightforward process that involves isolating the variable by performing the same operations on both sides of the equation. By following the steps outlined in this guide, you can solve a wide range of linear equations. The key is to remain consistent and perform operations in the correct order. With practice, you will become more proficient in solving these types of equations.

Remember, the more you practice, the better you will get at solving linear equations. Use the resources mentioned in this article to help you along the way. Happy problem-solving!