Solving the Equation 8x 45 - x: A Step-by-Step Guide for Algebra Students
Understanding and solving basic algebraic equations is a fundamental skill for students learning algebra. Whether you are a beginner or looking to brush up on your algebra skills, this guide will walk you through the process of solving the equation 8x 45 - x.
Introduction to the Equation
The equation we are dealing with is 8x 45 - x. This type of equation is called a linear equation because the highest power of the variable is one. The goal is to find the value of the variable x that satisfies the equation.
Solving the Equation Step-by-Step
Let us start by solving the equation in detail:
Step 1: Isolate the Variable on One Side of the Equation
First, add x to both sides of the equation to combine like terms:
8x x 45 - x x
This simplifies to:
9x 45
Step 2: Solve for the Variable
Next, divide both sides of the equation by 9 to isolate x:
9x / 9 45 / 9
This simplifies to:
x 5
The solution to the equation 8x 45 - x is x 5.
Verification
To ensure that the solution is correct, we can substitute x 5 back into the original equation and check if it holds true:
8(5) 45 - 5
This simplifies to:
40 40
Since the left side equals the right side, we have verified that x 5 is indeed the correct solution.
Conclusion
By following these step-by-step instructions, you have successfully solved the equation 8x 45 - x. It is crucial to always check your solution by substituting it back into the original equation. This practice will help you avoid mistakes and build confidence in your algebra skills.
Further Practice
For more practice and to further develop your algebra skills, consider solving similar equations such as 10y 50 - y, 7z 35 - 3z, or 9w 99 - w. Each of these equations follows the same steps: isolate the variable, combine like terms, and solve to find the value of the variable.
Remember, practice is key in mastering algebra. Keep practicing and referring to these types of exercises to improve your understanding and ability to solve linear equations.