Solving Equations with Variables: A Comprehensive Guide

Mathematics is a fundamental subject that underpins numerous areas of study and practical applications. Understanding how to solve equations with variables, such as 5x 3 1 - 17, is a crucial skill. This article will walk you through the process of solving these types of equations step-by-step, providing clear explanations and examples.

Solving the Equation 5x 3 1 - 17

Let's begin with the equation 5x 3 1 - 17. The goal is to isolate the variable x on one side of the equation. Here's a detailed breakdown of the steps:

Rearrange the equation to isolate the term with the variable. Start by simplifying the right side of the equation: 5x 3 1 - 17 Simplify the right side. Combine the constants on the right side: 5x 3 -16 Isolate the term with the variable. Subtract 3 from both sides to move the constant to the right side: 5x -19 Solve for x. Divide both sides by 5 to isolate x: x -19 / 5 Calculate the value of x. Perform the division: x -3.8

So, the value of x is -3.8.

Additional Examples

Example 1: 5x - 3 1 - 17

Let's solve another equation to solidify your understanding:

Rearrange the equation. Simplify the right side: 5x - 3 -16 Isolate the term with the variable. Add 3 to both sides: 5x -13 Solve for x. Divide both sides by 5: x -13 / 5 Calculate the value of x. Perform the division: x -2.6

Example 2: x - 3x -10 - 5

Another common form of equation involves combining like terms:

Simplify the left side. Combine the terms involving x on the left side: -2x -15 Solve for x. Divide both sides by -2: x 15 / 2 Calculate the value of x. Perform the division: x 7.5

Conclusion

Solving algebraic equations is a fundamental skill in mathematics and is crucial for advancing in subjects like calculus, physics, and engineering. By following the steps outlined in this article, you can confidently tackle equations involving variables. Practice is key to mastering these skills, so continue to solve similar problems to ensure you are comfortable with the process.