Solving a Simple Linear Equation: Decoding the Value of x in 5x - 3 7

Understanding basic algebraic equations like 5x - 3 7 is fundamental to grasping more advanced mathematical concepts. Let's break down the process of solving this equation to find the value of x.

Step-by-Step Guide to Solving the Equation

What's the Equation?

Given: 5x - 3 7

Let's Solve for x

Add 3 to Both Sides

To eliminate the -3 on the left-hand side, we add 3 to both sides of the equation. This gives us the following equation:

5x - 3 3 7 3

5x 10

This simplification helps us concentrate on finding the value of x by isolating it from the constant term.

Divide Both Sides by 5

To isolate x, divide both sides of the equation by 5:

5x / 5 10 / 5

x 2

This final step confirms that the value of x is 2. So, x 2 is the solution to the equation 5x - 3 7.

Alternative Methods

There are several ways to solve this equation. Here are a couple of alternative methods:

Multiplication and Subtraction Method

You can directly manipulate the equation as follows:

5x - 3 7 Add 3 to both sides:

5x 10 Divide both sides by 5:

x 2

Combination of Addition and Division

Another way to solve it is to combine the steps into a single operation:

5x - 3 7 Add 3 to both sides:

5x 10 Divide both sides by 5:

x 2

Conclusion

Understanding how to solve such equations is crucial for building a strong foundation in algebra. The values of x we discussed—obtained by various methods—are consistent and confirm that the correct solution is x 2. Practicing more problems will sharpen your skills and make solving these types of equations more intuitive.