Question

joe has a tree in his backyard. the tree grows 35 centimeters each year. since the tree started growing, joe has trimmed 22 centimeters off its height. the goal for the trees height is given by $35x - 22 geq 258$, 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.

Explanation:

Step1: Add 22 to both sides

$$35x-22 + 22\geq258 + 22$$
$$35x\geq280$$

Step2: Divide both sides by 35

$$\frac{35x}{35}\geq\frac{280}{35}$$
$$x\geq8$$

To graph \(x\geq8\) on the number line: Place a closed circle (since the inequality is \(\geq\)) at \(x = 8\) and draw a line to the right of \(8\) to represent all values of \(x\) that are greater than or equal to \(8\).

Answer:

The solution of the inequality \(35x-22\geq258\) is \(x\geq8\). On the number - line, there is a closed circle at \(8\) and a line extending to the right from \(8\).