Question

tony has a tree in his backyard. the tree grows 35 centimeters each year. since the tree started growing, tony 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. ○ to meet the goal, the tree must be more than centimeters tall. this will take less than years. ○ to meet the goal, the tree must be more than centimeters tall. this will take more than years. ○ to meet the goal, the tree must be less than centimeters tall. this will take more than years.

Explanation:

Step1: Solve the inequality

Given \(35x - 22>258\).
Add \(22\) to both sides:
\(35x-22 + 22>258+ 22\)
\(35x>280\)
Divide both sides by \(35\):
\(x>\frac{280}{35}\)
\(x > 8\)

Step2: Analyze the meaning of the solution

The inequality \(35x-22>258\) is about the height of the tree. The left - hand side \(35x-22\) represents the height of the tree (after trimming). The right - hand side \(258\) is the target height. The variable \(x\) represents the number of years.

Since \(x>8\), it means that to meet the goal ( \(35x - 22>258\)), when we consider the height part \(35x-22\) (the height of the tree), and the solution for \(x\) (the number of years).

The goal is \(35x-22>258\). The height part: we can rewrite the original inequality as \(35x>258 + 22=280\) (by moving the constant term). The number of years \(x>8\)

Answer:

(a) The solution of the inequality \(35x-22>258\) is \(x > 8\). On the number - line, we use an open circle at \(x = 8\) and draw an arrow to the right.
(b) To meet the goal, the tree must be more than \(258\) centimeters tall. This will take more than \(8\) years.