From (2): $ \frac{4}{3} - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac{4}{3} = 5 - \frac{4}{3} = \frac{11}{3} $
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 $.
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
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: $$ c = rac{9}{3} + rac{2}{3} = rac{11}{3} $$
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
