Solving linear equations is a fundamental skill in mathematics, and one of the simplest forms of equations to solve is the linear equation in one variable. A linear equation in one variable is an equation in which the highest power of the variable is one. For instance, 2x + 2 = 3x is a linear equation in one variable. In this article, we will discuss how to solve the equation 2x + 2 = 3x with ease.
Understanding the Equation
Before we dive into solving the equation, it is essential to understand the components of the equation. The equation 2x + 2 = 3x consists of two sides, the left-hand side (LHS) and the right-hand side (RHS). The LHS consists of two terms, 2x and 2, while the RHS consists of a single term, 3x.
Isolating the Variable
To solve the equation, we need to isolate the variable x. This involves getting x alone on one side of the equation. To do this, we can use the properties of equality, which state that we can add, subtract, multiply, or divide both sides of an equation by the same value without changing the solution.
In this case, we can subtract 2x from both sides of the equation to get:
2x - 2x + 2 = 3x - 2x
This simplifies to:
2 = x
Checking the Solution
Once we have found the solution, it is essential to check it by plugging it back into the original equation. This ensures that the solution satisfies the equation.
Plugging x = 2 into the original equation, we get:
2(2) + 2 = 3(2)
This simplifies to:
4 + 2 = 6
Which is a true statement, confirming that x = 2 is indeed the solution.
Real-World Applications
Linear equations, like the one we solved, have numerous real-world applications. For instance, they can be used to model real-world phenomena, such as population growth, financial transactions, and physics problems.
Conclusion
In conclusion, solving linear equations, such as 2x + 2 = 3x, is a straightforward process that involves isolating the variable and checking the solution. By following these steps, we can easily solve linear equations and apply them to real-world problems.
Gallery of Printable Linear Equations
What is a linear equation?
+A linear equation is an equation in which the highest power of the variable is one.
How do you solve a linear equation?
+To solve a linear equation, you need to isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
What is the purpose of checking the solution?
+Checking the solution ensures that the solution satisfies the equation and is the correct solution.
We hope you found this article helpful in solving linear equations with ease. If you have any further questions or need assistance, please don't hesitate to ask.