3n + 4(3.60 - 2n) = 7.80 - Decision Point
Solving the Equation: 3n + 4(3.60 - 2n) = 7.80
A Step-by-Step Guide to Solving Linear Equations
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 Context
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.
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Key Insights
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
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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:
