From (2): $ \frac43 - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac43 = 5 - \frac43 = \frac113 $ - AIKO, infinite ways to autonomy.
Solving the Equation: $ rac{4}{3} - 2 + c = 3 $ Step by Step
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
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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 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
