Question

aldo has a tree in his backyard. the tree grows 45 centimeters each year. since the tree started growing, aldo has trimmed 22 centimeters off its height. the goal for the trees height is given by 45x - 22≥248, 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 at least centimeters tall. this will take at most years. to meet the goal, the tree must be at least centimeters tall. this will take at least years. to meet the goal, the tree must be at most centimeters tall. this will take at least years.

Explanation:

Step1: Add 22 to both sides

$45x-22 + 22\geq248 + 22$
$45x\geq270$

Step2: Divide both sides by 45

$\frac{45x}{45}\geq\frac{270}{45}$
$x\geq6$

To graph on the number - line, we use a closed circle at 6 (because the inequality is $\geq$) and draw an arrow to the right.

For part (b), since $x\geq6$ represents the number of years the tree grows, to meet the goal, the tree must be at least 248 centimeters tall (from the original inequality $45x - 22\geq248$). This will take at least 6 years.

Answer:

(a) Solution of the inequality: $x\geq6$. On the number - line, place a closed circle at 6 and draw an arrow to the right.
(b) To meet the goal, the tree must be at least 248 centimeters tall. This will take at least 6 years.