2(3) + 3r = 12 - Abu Waleed Tea
Solving the Equation: 2(3) + 3r = 12
Solving the Equation: 2(3) + 3r = 12
Understanding how to solve linear equations is fundamental in algebra and forms the basis for many advanced math applications. One such equation frequently studied is 2(3) + 3r = 12. While seemingly simple, mastering this equation helps build strong problem-solving skills. In this article, we’ll walk through the step-by-step process of solving 2(3) + 3r = 12, explain the algebra behind it, and highlight common pitfalls and best practices.
Understanding the Context
What Does the Equation 2(3) + 3r = 12 Mean?
The expression 2(3) + 3r = 12 combines constants, multiplication, and a variable, which alters how we approach solving for r. Parentheses must be evaluated first, followed by multiplication before addition or equating.
Step-by-Step Solution
Key Insights
Step 1: Evaluate the Multiplication Inside Parentheses
Start by simplifying the expression inside the parentheses:
2(3) = 6
Now rewrite the equation:
6 + 3r = 12
```
Step 2: Isolate the Variable Term
Subtract 6 from both sides to eliminate the constant on the left:
6 + 3r - 6 = 12 - 6 Divide both sides by 3:
3r = 6
Step 3: Solve for r
3r ÷ 3 = 6 ÷ 3
r = 2
Final Answer
r = 2
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📰 So $ 2x = \frac{\pi}{4} \Rightarrow x = \frac{\pi}{8} $, and $ 2x = \frac{3\pi}{4} \Rightarrow x = \frac{3\pi}{8} $. 📰 Both values lie in $ (0, \pi) $. 📰 Therefore, the solutions are $ \boxed{\frac{\pi}{8},\ \frac{3\pi}{8}} $.Final Thoughts
Why This Equation Matters
While 2(3) + 3r = 12 is a basic linear equation, solving it introduces key algebraic concepts:
- Order of operations: Parentheses before multiplication
- Isolating variables: Moving constants to the opposite side
- Balancing both sides: Maintaining equation integrity by performing identical operations
These skills are essential for solving more complex equations in algebra, such as those involving multiple variables or higher-degree polynomials.
Tips for Solving Similar Equations
- Always simplify expressions inside parentheses first.
- Perform multiplication or division before addition or subtraction.
- Keep one side of the equation isolated at each step.
- Check your answer by substituting r = 2 back into the original equation:
2(3) + 3(2) = 6 + 6 = 12 ✔
Related Topics
- Linear equations with one variable
- Solving equations with coefficients
- Algebraic expression simplification
- Equation balancing techniques
