What Is The Solution Of 3X + 5 = 2X + 7?

Introduction

Equations are the foundation of mathematics. They are used to represent relationships between mathematical expressions. In solving equations, the goal is to find the value of the variable that makes the equation true. In this article, we will discuss how to solve the equation 3x + 5 = 2x + 7.

Understanding the Equation

The equation 3x + 5 = 2x + 7 is a linear equation. A linear equation is an equation that can be represented by a straight line on a graph. The equation has two sides, the left-hand side and the right-hand side. The left-hand side of the equation consists of the expression 3x + 5, while the right-hand side consists of the expression 2x + 7.

Solving the Equation

To solve the equation 3x + 5 = 2x + 7, we need to isolate the variable x on one side of the equation. We can do this by subtracting 2x from both sides of the equation. This will give us: 3x + 5 - 2x = 2x + 7 - 2x Simplifying the equation, we get: x + 5 = 7 Next, we need to isolate x by subtracting 5 from both sides of the equation. This will give us: x + 5 - 5 = 7 - 5 Simplifying the equation, we get: x = 2 Therefore, the solution to the equation 3x + 5 = 2x + 7 is x = 2.

Checking the Solution

To check if our solution is correct, we can substitute x = 2 back into the original equation and see if it makes the equation true. Substituting x = 2 into the equation 3x + 5 = 2x + 7, we get: 3(2) + 5 = 2(2) + 7 Simplifying the equation, we get: 6 + 5 = 4 + 7 11 = 11 Since 11 equals 11, our solution is correct.

Conclusion

In conclusion, the solution to the equation 3x + 5 = 2x + 7 is x = 2. To solve the equation, we isolated the variable x on one side of the equation by subtracting 2x from both sides and then subtracting 5 from both sides. We checked our solution by substituting x = 2 back into the original equation and verifying that it makes the equation true.