2/3x-2=3/4 Rewritten Without Fractions?

To rewrite the equation 2/3x – 2 = 3/4 without fractions, we’ll follow these steps:

Step 1: Eliminate the fractions. Step 2: Solve for x.

Let’s break it down:

Step 1: Eliminate the fractions

To eliminate fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is 12. This will clear the fractions.

(12) * (2/3x – 2) = (12) * (3/4)

Now, distribute the 12 to both terms on the left side of the equation:

(12) * (2/3x) – (12) * 2 = (12) * (3/4)

This simplifies to:

(8x) – 24 = 9

Step 2: Solve for x

Now that we’ve eliminated the fractions, we can proceed to solve for x. Start by isolating the term with x on one side of the equation.

Add 24 to both sides to get rid of the -24 on the left side:

8x – 24 + 24 = 9 + 24

This simplifies to:

8x = 33

Now, to isolate x, divide both sides by 8:

(8x) / 8 = 33 / 8

x = 33/8

So, the equation 2/3x – 2 = 3/4, when rewritten without fractions, is:

8x – 24 = 33

And the solution for x is:

x = 33/8

Now, let’s discuss how to turn this solution into a 1000-word blog post. To expand on this topic and create a comprehensive blog post, you can consider the following structure:

Title: Solving Equations with Fractions: Eliminating Fractions and Finding Solutions

Introduction (150 words):

• Start with an engaging hook to introduce the importance of solving equations.
• Briefly mention that fractions in equations can be challenging and that this blog post will show how to eliminate them to find solutions.
• Provide an outline of what readers can expect from the blog post.

Understanding the Equation (200 words):

• Explain what the given equation 2/3x – 2 = 3/4 means.
• Describe why equations with fractions can be tricky and intimidating.
• Discuss the importance of simplifying equations for easier solving.

Step-by-Step Solution (300 words):

• Break down the steps for eliminating fractions in the equation:
  • Multiply both sides by the LCM of the denominators (12 in this case).
  • Distribute the LCM to both sides.
• Provide a detailed example, as shown above, with calculations and explanations.
• Emphasize the importance of maintaining equality throughout the process.

Solving for x (200 words):

• Explain the process of solving for x after eliminating fractions.
• Discuss the importance of isolating x on one side of the equation.
• Show how to add, subtract, multiply, or divide as needed to isolate x.
• Present the final solution, x = 33/8.

Practical Applications (150 words):

• Discuss real-life scenarios where solving equations with fractions is useful.
• Show how the skills learned in this blog post can be applied to solve practical problems in fields like engineering, science, and finance.

Conclusion (100 words):

• Summarize the key points discussed in the blog post.
• Reiterate the importance of understanding and solving equations with fractions.
• Encourage readers to practice and apply the knowledge gained from this post in their own math endeavors.

Additional Tips (50 words):

• Provide additional tips and resources for further practice.
• Mention other related topics readers might find interesting.

By following this structure and elaborating on each section, you can easily create a 1000-word blog post that not only explains how to rewrite equations without fractions but also provides valuable context and applications for the concept.