Solving the Equation: 3n + 4(3.60 - 2n) = 7.80
A Step-by-Step Guide to Solving Linear Equations
When faced with equations in algebra, clarity and systematic problem-solving are key. Today, we’ll break down how to solve the equation:
3n + 4(3.60 - 2n) = 7.80, step-by-step, to help you understand the process of simplifying and isolating variables.
Understanding the Equation
The equation is:
3n + 4(3.60 - 2n) = 7.80
This involves distributive property and combining like terms — essential skills in solving linear equations.
Step 1: Distribute the 4
Distribute 4 across the terms inside the parentheses:
> 3n + 4 × 3.60 − 4 × 2n = 7.80
3n + 14.40 − 8n = 7.80
Step 2: Combine Like Terms
Combine the terms with n:
> (3n − 8n) + 14.40 = 7.80
−5n + 14.40 = 7.80
Step 3: Isolate the Variable Term
Subtract 14.40 from both sides:
> −5n = 7.80 − 14.40
−5n = −6.60
Step 4: Solve for n
Divide both sides by −5:
> n = −6.60 ÷ (−5)
n = 1.32
Final Answer
✅ n = 1.32
Why This Matters
Mastering such equations strengthens foundational algebra skills. These linear expressions appear frequently in real-world applications—from budgeting and engineering calculations to computer programming logic.
Tips for Solving Linear Equations Quickly
- Always distribute first to clear parentheses.
- Group and combine like terms to simplify.
- Keep the variable terms on one side and constants on the other.
- Always isolate the variable by performing inverse operations.
HTML-Ready Summary (for SEO optimization)
</blockquote> <!-- SEO-Optimized Article Structure --> <h1>How to Solve 3n + 4(3.60 - 2n) = 7.80—Step-by-Step Guide</h1> <p>Mastering linear equations is essential for students and anyone working with mathematical models. In this guide, we solve <strong>3n + 4(3.60 - 2n) = 7.80</strong> step-by-step using distribution, combining like terms, and isolating the variable.</p> <p> <strong>Step 1: Distribute 4</strong><br/> 3n + 14.40 − 8n = 7.80 <strong>Step 2: Combine like terms</strong><br/> −5n + 14.40 = 7.80 <strong>Step 3: Isolate variable</strong><br/> −5n = −6.60 → n = 1.32 <strong>Final Answer:</strong> <code>n = 1.32</code> <strong>Boost Algebra Skills:</strong> Use this method anytime you encounter equations involving parentheses and coefficients.<br/>
Keywords included for SEO:
- linear equations
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- 3n + 4(3.6 - 2n)
- n = 1.32
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By understanding this process, you’ll solve similar equations with confidence and precision!
