$f(5) = 6(125) - 36(25) + 54(5) = 750 - 900 + 270 = 120$ - Decision Point
Solving $ f(5) = 6(125) - 36(25) + 54(5) $: A Step-by-Step Breakdown with Calculation and Explanation
Solving $ f(5) = 6(125) - 36(25) + 54(5) $: A Step-by-Step Breakdown with Calculation and Explanation
Understanding how to evaluate expressions involving function evaluation—like $ f(5) = 6(125) - 36(25) + 54(5) $—is essential for mastering algebra and simplifying complex equations. This article guides you through solving this specific expression step-by-step, explores its mathematical significance, and explains the final result clearly.
Understanding the Context
What Is the Expression $ f(5) = 6(125) - 36(25) + 54(5) $?
At first glance, the formula $ f(5) = 6(125) - 36(25) + 54(5) $ defines $ f $ as an input-dependent equation evaluated at $ x = 5 $. Though $ f(x) $ isn’t explicitly given as a function, interpretations include evaluation at specific values, substitution in algebraic expressions, or even a model for real-world problems.
In this case, rather than treating $ f(5) $ as a function, we resolve the arithmetic expression directly by computing each term and combining the results.
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Key Insights
Step 1: Break Down the Multiplication Within the Expression
Evaluate each product separately:
- $ 6(125) = 750 $
- $ 36(25) = 900 $
- $ 54(5) = 270 $
Step 2: Substitute Back Into the Equation
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Replace each term in the original expression:
$$
f(5) = 750 - 900 + 270
$$
Step 3: Perform the Arithmetic Operations
Rearranged for clarity:
$$
f(5) = 750 - 900 + 270 = (750 + 270) - 900 = 1020 - 900 = 120
$$
Final Result: $ f(5) = 120 $
Thus, the value of the expression at $ x = 5 $ is 120, confirmed by step-by-step simplification:
$$
f(5) = 6(125) - 36(25) + 54(5) = 750 - 900 + 270 = 120
$$
