Questions: David is planting a rectangular garden in his backyard. He wants the length of the garden to be 4 yards. The area of the garden must be less than 32 square yards. (David doesn't want to buy any more soil.) Write an inequality that describes the possible widths (in yards) of the garden. Use w for the width of the rectangular garden.

Solution Steps

To find the possible widths of the garden, we need to use the formula for the area of a rectangle, which is length times width. Given that the length is 4 yards and the area must be less than 32 square yards, we can set up an inequality: \(4 \times w < 32\). Solving this inequality will give us the possible values for the width \(w\).

To determine the possible widths \( w \) of the rectangular garden, we start with the area formula for a rectangle, which is given by: \[ \text{Area} = \text{Length} \times \text{Width} \] Given that the length is \( 4 \) yards and the area must be less than \( 32 \) square yards, we can set up the inequality: \[ 4w < 32 \]

Next, we solve the inequality for \( w \): \[ w < \frac{32}{4} \] This simplifies to: \[ w < 8 \]

Since \( w \) represents a physical dimension (width), it must also be greater than \( 0 \). Therefore, we can express the range of possible widths as: \[ 0 < w < 8 \]

Final Answer