Solving the Equation 3x-58 for x
Algebra offers a systematic approach to solving equations for unknown variables. The example we will explore in this article is the equation 3x-58. Our goal is to find the value of x. This process is crucial for many areas of mathematics and its applications. Let's break down the steps involved in solving this equation.
Introduction to the Equation
The equation 3x-58 involves a variable x, a coefficient (3), a constant (-5), and an equal sign (8). Our objective is to isolate the variable x on one side of the equation. This process is called solving the equation for the variable.
Step-by-Step Solution
To solve 3x-58 for x, we will follow a series of algebraic operations:
Subtract 5 from both sides of the equation:Initial equation: 3x-58
Subtract 5 from both sides: 3x-5-58-5
Simplify:
3x-103
Combine like terms on the left side:Combine -5-5 to get -10
3x-103 simplifies to 3x-53
Add 5 to both sides to isolate the term with x:3x-5 53 5
Simplify:
3x8
Divide both sides by 3 to solve for x:3x/38/3
Simplify:
x8/3
Therefore, the value of x that satisfies the equation 3x-58 is x8/3 or approximately 2.67.
Verification
To ensure the solution is correct, we can substitute x8/3 back into the original equation:
3(8/3)-58
(24/3)-58
8-58
38
The equation holds true, confirming that our solution is correct.
Conclusion
Understanding and mastering the process of solving algebraic equations is essential in many fields. Whether you are a student, a professional, or simply someone interested in mathematics, the ability to solve equations like 3x-58 can be very helpful. By following the steps outlined in this article, you can systematically approach and solve such equations for any variable.