Solving the Equation: $ rac{4}{3} - 2 + c = 3 $ Step by Step

Understanding how to solve linear equations is essential in algebra, and today we’ll walk through a clear example: solving for $ c $ in the equation
$ rac{4}{3} - 2 + c = 3 $. This problem demonstrates fundamental algebraic manipulation, including combining fractions, integers, and isolating the variable $ c $.

Understanding the Context

Step 1: Simplify the left-hand side expression

We begin by simplifying $ rac{4}{3} - 2 + c $. To combine the constants, express $ 2 $ as a fraction with denominator 3:
$$
2 = rac{6}{3}
$$
Now substitute back:
$$
rac{4}{3} - rac{6}{3} + c
$$
Subtract the fractions:
$$
rac{4 - 6}{3} + c = - rac{2}{3} + c
$$
So the equation becomes:
$$
- rac{2}{3} + c = 3
$$

Step 2: Isolate $ c $ by adding $ rac{2}{3} $ to both sides

From (2): $ \frac{4}{3} - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac{4}{3} = 5 - \frac{4}{3} = \frac{11}{3} $

Key Insights

To solve for $ c $, add $ rac{2}{3} $ to both sides:
$$
c = 3 + rac{2}{3}
$$

Step 3: Express the right-hand side as a single fraction

Convert $ 3 $ to a fraction with denominator 3:
$$
3 = rac{9}{3}
$$
Then:
$$
c = rac{9}{3} + rac{2}{3} = rac{11}{3}
$$

Continue Reading

But to match the format and intent—clickbait style with SEO optimization and deep mathematical insight:
Question: What is the maximum value of \( \left| \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) \right| \) for a unit vector \( \mathbf{v} \), given \( \mathbf{w} = \langle 1, 0, 1 \rangle \) and \( \mathbf{u} = \langle 0, 1, 2 \rangle \)?
Solution: The expression \( \left| \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) \right| \) depends on the magnitude of the binormal vector. Compute \( \mathbf{w} \times \mathbf{u} = \left\langle -1, -2, 1 \right\rangle \), so

🔗 Related Articles You Might Like:

📰 This Secret Onion Rings Recipe Is lighter, Crisier and Impossible to Resist 📰 The Only Onion Rings That Really Stick Together—Here’s the Shocking Truth 📰 Transform Bland Snacks Into Onion Rings Masterpieces with This Whispered Secret 📰 Zeldas Ocarina Of Time Secret Walkthrough You Need To Watch This 📰 Zeldas Phantom Hourglass Secrets Shock Fans You Need This Guide Before Its Too Late 📰 Zeldas Skyward Sword The Surveillance Tool You Never Knew Existed 📰 Zeldris Reveals The Hidden Powers That Every Fan Has Been Waiting For 📰 Zeldris Unleashed The Ultimate Secret That Im Still Shocked About 📰 Zelle Logo Myth Busted The Real Story Behind One Of The Most Recognized Symbols Today 📰 Zelle Logo Secrets Why This Simple Design Changed Digital Payments Forever 📰 Zemeckis Movies That Shook The Worldthese 5 Classics Are Unmissable 📰 Zemo Breakthrough Why Millions Are Swarming This Breaking Innovation 📰 Zemo Hacks Everything From Sustainable Tech To Content Creationready To Discover 📰 Zemo Marvel Secrets Inside The Revolution Thats Changing Games Forever 📰 Zemo Marvel Shock What This Game Changer In Tech Will Define 2025 📰 Zemo Marvel Unleashed The Hidden Features Adventure Youve Been Searching For 📰 Zemo Mystery Solved The Hidden Gigabytes Behind The Hype 📰 Zemo Unveiled The Revolutionary Secret Thats Taking The Market By Storm

Final Thoughts

Final Result

$$
oxed{c = rac{11}{3}}
$$

This method highlights key algebraic techniques: combining rational numbers, isolating variables, and simplifying expressions. Mastering such steps helps build stronger problem-solving skills for more complex equations in mathematics and science applications.

Key Takeaways:

  • Always convert integers to fractions for consistent arithmetic.
  • Combine like terms carefully.
  • Isolate the variable step-by-step to solve equations.
  • Express final answers in simplest form.

Understanding these steps ensures clarity and accuracy in solving algebraic expressions and equations critical to advancing mathematical proficiency.

Keywords: solving linear equations, algebra 101, how to solve for c, fraction arithmetic, algebra problems with variables, step-by-step equation solving, math tutorial