Question

Alonzo has a tree in his backyard. The tree grows 50 centimeters each year. Since the tree started growing, Alonzo has trimmed 24 centimeters off its height. The goal for the tree's height is given by 50x - 24 > 276, 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

Answer 1

Choose and complete the statement that best describes the solution.
1. •To meet the goal, the tree must be more than (?) centimeters tall. This will take less than (?) years.
2. To meet the goal, the tree must be more than (?) centimeters tall. This will take more than (?) years.
3. To meet the goal, the tree must be less than (?) centimeters tall. This will take more than (?) years.

Answer 2

To solve the inequality given by \( 50x - 24 > 276 \), we start by isolating \( x \).

1. Add 24 to both sides:
\[
50x - 24 + 24 > 276 + 24
\]
\[
50x > 300
\]

2. Next, divide both sides by 50:
\[
x > \frac{300}{50}
\]
\[
x > 6
\]

The solution to the inequality is \( x > 6 \).

### Graphing the Solution:

On a number line, we would represent this as an open circle at \( 6 \) (indicating that \( 6 \) is not included in the solution) and shade to the right to indicate all values greater than \( 6 \).

```
Number line:
<--|---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8 9

(--------------------------->
```

The open circle at \( 6 \) signifies that \( x \) can take any value greater than \( 6 \).