Question

kareem has a tree in his backyard. the tree grows 30 centimeters each year. since the tree started growing, kareem has trimmed 18 centimeters off its height. the goal for the trees height is given by ( 30x - 18>252 ), 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 more than years. 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 less than centimeters tall. this will take more than years.

Explanation:

Step1: Solve the inequality \(30x - 18>252\)

Add \(18\) to both sides of the inequality:
\(30x-18 + 18>252+18\)
\(30x>270\)

Step2: Isolate \(x\)

Divide both sides of the inequality by \(30\):
\(x>\frac{270}{30}\)
\(x > 9\)

For graphing on the number - line:

• Place an open circle at \(x = 9\) (because the inequality is \(>\), not \(\geq\)).
• Shade the region to the right of \(x = 9\) since \(x\) is greater than \(9\).

Step3: Analyze the statement for part (b)

The goal is \(30x-18>252\). The left - hand side \(30x - 18\) represents the height of the tree. So the tree must be more than \(252\) centimeters tall.
We found that \(x>9\), which means it will take more than \(9\) years.

Answer:

(a) The solution of the inequality \(30x - 18>252\) is \(x>9\). On the number - line, place an open circle at \(9\) and shade to the right.
(b) To meet the goal, the tree must be more than \(252\) centimeters tall. This will take more than \(9\) years.