$f(5) = 6(125) - 36(25) + 54(5) = 750 - 900 + 270 = 120$

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.

$f(5) = 6(125) - 36(25) + 54(5) = 750 - 900 + 270 = 120$

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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Final Thoughts

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:

$$
f(5) = 6(125) - 36(25) + 54(5) = 750 - 900 + 270 = 120
$$