Question

1. the length of a rectangle is eight more than twice its width. if the length is less than 34, then what is the width? variable:__ inequality: solution:__ 5. dennis has sold $40 worth of chocolate bars for a fundraiser. if he sells over $175

Explanation:

Step1: Define the variable

Let $w$ be the width of the rectangle.

Step2: Express the length in terms of the width

The length $l$ is eight more than twice the width, so $l = 2w + 8$.

Step3: Set up the inequality

Since the length is less than 34, we have the inequality $2w+8<34$.

Step4: Solve the inequality

Subtract 8 from both sides: $2w+8 - 8<34 - 8$, which simplifies to $2w<26$. Then divide both sides by 2: $\frac{2w}{2}<\frac{26}{2}$, so $w < 13$.

Answer:

Variable: $w$ (width of the rectangle)
Inequality: $2w + 8<34$
Solution: $w<13$