Solve one-step inequalities and represent solutions on a number line.
Match a context to the right one-step inequality
Problem
A backpack weighs \(8~\text{pounds}\) and may weigh no more than \(20~\text{pounds}\). Let \(w\) be the nonnegative added weight. Which inequality below models the limit? Choose it, then solve using only values that make sense in context.
A. \(8~+~w~<~20\) B. \(8~+~w~\le~20\) C. \(8~+~w~\ge~20\)
Big Picture
What this problem is really about
The backpack’s total is its current eight pounds plus w pounds added. “No more than” points toward smaller totals and includes the twenty-pound limit, so the model needs an inclusive upper bound. Solve for the remaining capacity, then combine that upper bound with the contextual lower bound that added weight cannot be negative.
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