Question

josh has a tree in his backyard. the tree grows 25 centimeters each year. since the tree started growing, josh has trimmed 16 centimeters off its height. the goal for the trees height is given by $25x - 16 \geq 234$, 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 at least \square centimeters tall. this will take at most \square years.\
\bigcirc to meet the goal, the tree must be at least \square centimeters tall. this will take at least \square years.\
\bigcirc to meet the goal, the tree must be at most \square centimeters tall. this will take at least \square years.

Explanation:

Step1: Add 16 to both sides

$25x - 16 + 16 \geq 234 + 16$
$25x \geq 250$

Step2: Divide by 25

$\frac{25x}{25} \geq \frac{250}{25}$
$x \geq 10$

Step3: Analyze the inequality meaning

The left side $25x - 16$ is the tree's height, so the goal is at least 234 cm. The solution $x \geq 10$ means at least 10 years.

Step4: Select the correct statement

Choose the option: "To meet the goal, the tree must be at least 234 centimeters tall. This will take at least 10 years."

For the number line graph: Place a closed dot at 10 and shade to the right.

Answer:

(a) $x \geq 10$
(b) To meet the goal, the tree must be at least 234 centimeters tall. This will take at least 10 years.