Question

alan has a tree in his backyard. the tree grows 35 centimeters each year. since the tree started growing, alan has trimmed 22 centimeters off its height. the goal for the trees height is given by 35x - 22 > 258, where x is the number of years the tree grows. complete the parts below. (a) solve the given inequality and graph the solution on the number line below. (b) choose and complete the statement that best describes the solution. \bigcirc to meet the goal, the tree must be more than \square centimeters tall. this will take less than \square years. \bigcirc to meet the goal, the tree must be more than \square centimeters tall. this will take more than \square years. \bigcirc to meet the goal, the tree must be less than \square centimeters tall. this will take more than \square years.

Explanation:

Step1: Add 22 to both sides

\(35x - 22 + 22 > 258 + 22\)
\(35x > 280\)

Step2: Divide by 35

\(\frac{35x}{35} > \frac{280}{35}\)
\(x > 8\)

Step3: Analyze the inequality meaning

The left side \(35x - 22\) is the tree's height, so it needs to be more than 258 cm. Since \(x > 8\), it takes more than 8 years.

Answer:

(a) \(x > 8\)
(b) To meet the goal, the tree must be more than 258 centimeters tall. This will take more than 8 years.