Solving Linear Equations: 2x - 1 = 5 - x
In this article, we will explore how to solve a simple linear equation, specifically the equation 2x - 1 = 5 - x. Linear equations are a fundamental concept in algebra and are used to solve a wide range of problems.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable (in this case, x) is 1. Linear equations can be written in the form:
ax + b = c
where a, b, and c are constants, and x is the variable.
Solving the Equation
Now, let's solve the equation 2x - 1 = 5 - x. To do this, we can add x to both sides of the equation, which results in:
2x - 1 + x = 5 - x + x
This simplifies to:
3x - 1 = 5
Next, we can add 1 to both sides of the equation to get:
3x = 5 + 1
3x = 6
Finally, we can divide both sides of the equation by 3 to solve for x:
x = 6/3
x = 2
Therefore, the solution to the equation 2x - 1 = 5 - x is x = 2.
Conclusion
In this article, we have solved the linear equation 2x - 1 = 5 - x using basic algebraic operations. By adding x to both sides of the equation, adding 1 to both sides, and dividing both sides by 3, we were able to isolate the variable x and find its value. This is a simple example of how to solve a linear equation, and similar techniques can be used to solve more complex equations.
