Question

Latoya is pumping water into a tank at a rate of 16 liters per minute. Since she started pumping water, 14 liters has splashed out of the tank. Her goal is given by 16x - 14≤66, where x is the number of minutes she pumps water into the tank.
(a) Complete the parts below. solve the given inequality and graph the solution on the number line below
0-2-4-6-8-10-12-14-16-18-20-22-24-26-28-30

Answer 1

To solve the inequality \( 16x - 14 \leq 66 \), we will first isolate \( x \).

1. **Add 14 to both sides**:
\[
16x \leq 66 + 14
\]
\[
16x \leq 80
\]

2. **Divide both sides by 16**:
\[
x \leq \frac{80}{16}
\]
\[
x \leq 5
\]

The solution to the inequality is \( x \leq 5 \). This means Latoya can pump water for up to 5 minutes.

Next, we will graph this solution on a number line.

### Number Line Graph:
- We will mark 5 on the number line.
- We will indicate that the values of \( x \) can go down to negative infinity, all the way up to and including 5.

Here's the representation on the provided number line:

```
<--|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
0 2 4 5 6 8 10 12 14 16 18 20 22 24 26 28 30
[======)
```
- The bracket at 5 indicates that 5 is included in the solution (i.e., \( x \leq 5 \)).
- The solid line extending to the left indicates all values less than 5 are also included in the solution.

Thus, the complete solution is that Latoya can pump water for any number of minutes \( x \) that is less than or equal to 5 minutes.