Question

Raina is pumping water into an aquarium at a rate of Il liters per minute. The aquarium had 34 liters of water in it before she started. Her goal is given by 11x + 34 < 254, where x is the number of minutes she pumps water into the aquarium.
Complete the parts below.
(a) 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 \( 11x + 34 < 254 \), we'll first isolate \( x \).

1. Subtract 34 from both sides:
\[
11x < 254 - 34
\]
\[
11x < 220
\]

2. Next, divide both sides by 11:
\[
x < \frac{220}{11}
\]
\[
x < 20
\]

Thus, the solution to the inequality is \( x < 20 \).

### Graphing the solution on the number line:

To graph \( x < 20 \):

1. Draw a number line that includes numbers from 0 to 30.
2. Place an open circle at 20 (indicating that 20 is not included in the solution).
3. Shade all the values to the left of 20 to indicate that any value less than 20 is part of the solution.

Here’s a representation of how it would look:

```
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ● 21 22 23 24 25 26 27 28 29 30
```

- The open circle indicates that 20 is not included,
- The shaded line extends to the left of 20, showing all numbers less than 20 are included in the solution.