Solving Equations: A Step-by-Step Guide to Finding the Value of x

Introduction to Equations

Equations are a fundamental part of mathematics, allowing us to express relationships between quantities and solve for unknown values. In this article, we will explore in detail how to find the value of x in a variety of equations, with a specific focus on the example given: 2x 5 9.

Solving the Basic Equation 2x 5 9

The given equation is 2x 5 9. Our goal is to isolate x on one side to find its value.

Step 1: Subtract 5 from both sides

To eliminate the constant term on the left-hand side (LHS), we subtract 5 from both sides of the equation:

2x 5 - 5 9 - 5

This simplifies to:

2x 4

Step 2: Divide both sides by 2

Next, we divide both sides of the equation by 2 to isolate x:

2x / 2 4 / 2

This further simplifies to:

x 2

Therefore, the value of x is 2.

Alternative Methods to Solve the Equation

There are several alternative methods to arrive at the same solution. Let's explore them in detail:

Method 1: Move 5 to the RHS

We can also move the constant term to the right-hand side (RHS) to change the sign of 5, resulting in:

2x 9 - 5

Then, we simplify:

2x 4

And divide both sides by 2:

x 4 / 2

This results in:

x 2

Method 2: Direct Subtraction and Division

A straightforward approach is to subtract 5 from 9 and then divide the result by 2:

5x - 4 9

First, solve for 5x:

5x 9 4 13

Then, divide by 5:

x 13 / 5 2.6

Method 3: More Complex Equations

Let's consider a more complicated equation: 3x/5 - 2x 9.

Solution:

First, combine like terms:

3x/5 - 2x/1 9

Find the common denominator (5):

3x/5 - 1/5 9

Combine the fractions:

3x - 1 45

Simplify:

-7x 45

Divide by -7:

x 45 / -7 -6.43

Conclusion

In this article, we have explored various methods to find the value of x in the equation 2x 5 9. Whether you choose to subtract, divide, or manipulate the equation, the ultimate goal is to isolate x and find its value. Understanding these techniques is crucial for solving more complex equations in algebra.

Key Takeaways

1. Equations can be solved by isolating the variable on one side of the equation.

2. Moving terms to the other side changes their sign.

3. Divide both sides of the equation by the coefficient of the variable to solve for it.

4. Practice different methods to enhance problem-solving skills.