Solve 3x 4 7 4 5x 12

Solving the Equation: 3x + 4 = 7 - 4 + 5x + 12

This article will guide you through solving the algebraic equation 3x + 4 = 7 - 4 + 5x + 12. We'll break down the process step-by-step, making it easy to understand even for those new to algebra. Understanding how to solve equations like this is fundamental to mastering algebra and many other mathematical concepts. This process involves simplifying the equation and isolating the variable 'x'.

Understanding the Equation

Before we begin, let's simplify the right-hand side of the equation:

7 - 4 + 12 = 15

Therefore, our equation becomes:

3x + 4 = 15 + 5x

Step-by-Step Solution

Our goal is to isolate 'x' on one side of the equation. We can achieve this by performing the same operation on both sides, maintaining the equation's balance.

1. Subtract 3x from both sides:

This will remove the '3x' term from the left side.

3x + 4 - 3x = 15 + 5x - 3x

Simplifying, we get:

4 = 15 + 2x

2. Subtract 15 from both sides:

This isolates the term with 'x'.

4 - 15 = 15 + 2x - 15

Simplifying, we get:

-11 = 2x

3. Divide both sides by 2:

This isolates 'x'.

-11 / 2 = 2x / 2

Therefore, the solution is:

x = -11/2 or x = -5.5

Verification

To verify our solution, substitute x = -5.5 back into the original equation:

3(-5.5) + 4 = 7 - 4 + 5(-5.5) + 12

-16.5 + 4 = 3 - 27.5 + 12

-12.5 = -12.5

Since both sides are equal, our solution x = -5.5 is correct.

Key Concepts Used

• Combining like terms: Adding or subtracting terms with the same variable (e.g., 5x - 3x = 2x).
• Inverse operations: Using opposite operations (addition/subtraction, multiplication/division) to isolate the variable.
• Maintaining balance: Performing the same operation on both sides of the equation to keep it equal.

This method can be applied to solve a wide range of linear equations. Remember to always simplify the equation first before attempting to isolate the variable. Practice is key to mastering these techniques. Try solving similar equations to reinforce your understanding and build confidence in your algebraic skills. Understanding equation solving is a crucial stepping stone in higher-level mathematics.