From (2): $ \frac43 - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac43 = 5 - \frac43 = \frac113 $

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:
$$
c = rac{9}{3} + rac{2}{3} = rac{11}{3}
$$

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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.

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