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:

Explanation:

Step1: Define the variable

Let the width of the rectangle be $w$.

Step2: Express the length in terms of width

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

Step3: Set up the inequality

Given that 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 $2w<26$.
Divide both sides by 2: $\frac{2w}{2}<\frac{26}{2}$, so $w < 13$.

Answer:

The width $w$ satisfies the inequality $w<13$.