Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Create and solve a rational inequality from a constraint
Problem
A fixed cost of \(\$100\) is spread over \(x\) positive kilograms, so the average cost is \(100/x~\text{dollars}~\text{per}~\text{kilogram}\). Write and solve the rational inequality that keeps the average cost at most \(\$20~\text{per}~\text{kilogram}\), then report the context-valid solution set.
Big Picture
What this problem is really about
Spreading a fixed cost over more kilograms puts the positive quantity in the denominator, and “at most” creates an inclusive inequality. We’ll use the stated positive domain before clearing that denominator, which tells us the comparison direction stays unchanged, then check the boundary and which side makes the average cost smaller.
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