Question

a carpenter is building shelving units for a garage. a small shelf requires a total of 6 boards to build, while a large one uses 14 boards. he has up to 32 boards to use for this project. select the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of small shelving units y = the number of large shelving units 14x + 6y ≤ 32 6x + 14y ≤ 32 14x + 6y < 32 6x + 14y < 32

Explanation:

Step1: Determine boards for small shelves

Small shelf (x) uses 6 boards each, so total boards for small: $6x$.

Step2: Determine boards for large shelves

Large shelf (y) uses 14 boards each, so total boards for large: $14y$.

Step3: Total boards and inequality

Total boards used: $6x + 14y$. He has up to 32 boards (≤32), so $6x + 14y \leq 32$.

Answer:

B. \(6x + 14y \leq 32\) (assuming the second option is labeled B, with the text "6x + 14y ≤ 32")