Solving the Equation x/2 - 2 2x - 11: A Step-by-Step Guide for SEO-Optimized Content

Welcome to our guide on how to solve the algebraic equation x/2 - 2 2x - 11. This guide is designed to be accessible and educational, catering to beginners and intermediate learners alike. Whether you're preparing for a math exam or just curious about algebra, this article will walk you through the process with clear, actionable steps. By the end, you'll not only solve the equation but also understand the underlying concepts that make algebraic problem-solving possible.

Understanding the Equation: x/2 - 2 2x - 11

The equation we're dealing with is x/2 - 2 2x - 11. At first glance, it might seem a bit daunting, but don't worry! We'll break it down step by step. Our goal is to isolate the variable x so that we can find its value.

Step 1: Eliminating the Fraction

The first step is to eliminate the fraction x/2. To do this, we multiply every term in the equation by 2. This is a common technique in algebra, as it helps to clear the fraction and simplify the equation. Let's do this step by step:

2(x/2) - 2(2) 2(2x) - 2(11)

Simplifying both sides of the equation, we get:

x - 4 4x - 22

Step 2: Rearranging the Equation

Next, we need to rearrange the equation to group all terms involving x on one side and the constant terms on the other side. This is essential to isolate x. Here’s how we do it:

x - 4x -22 4

Simplifying the left side, we have:

-3x -18

Step 3: Solving for x

Now that we have -3x -18, we can solve for x by dividing both sides by -3. This step is straightforward:

x -18 / -3

Simplifying the right side, we get:

x 6

This is our final answer. To ensure the solution is correct, we can substitute x 6 back into the original equation:

x/2 - 2 2x - 11

6/2 - 2 2(6) - 11

3 - 2 12 - 11

1 1

Since both sides are equal, we have verified that x 6 is indeed the correct solution.

Conclusion

In summary, solving the equation x/2 - 2 2x - 11 involves several key steps: eliminating the fraction, rearranging the equation, solving for the variable, and verifying the solution. By following these steps, you can solve a wide range of algebraic equations with confidence. If you're looking for more resources on algebra or need help with similar problems, feel free to explore our website, where we offer a multitude of guides and tutorials to help you master the art of algebra.

Additional Resources

For further learning and more in-depth explanations, check out our collection of algebra lessons and practice problems. We also offer a variety of interactive tools and quizzes to help you reinforce your understanding of algebraic equations. Happy learning!