Question

Solve the inequality and graph the solution on the line provided.
3, x, minus, 8, is less than, minus, 20
3x−8<
−20

Answer 1

Let's solve the inequality \(3x - 8 < -20\).

1. Start by adding 8 to both sides of the inequality:
\[
3x - 8 + 8 < -20 + 8
\]
This simplifies to:
\[
3x < -12
\]

2. Next, divide both sides by 3:
\[
x < -4
\]

So, the solution to the inequality is:
\[
x < -4
\]

Now, we can graph the solution on a number line:

1. Draw a horizontal line to represent the number line.
2. Identify the point \(-4\) on the line.
3. Since \(x\) can be any number less than \(-4\), draw an open circle at \(-4\) (indicating that \(-4\) is not included in the solution).
4. Shade the line to the left of \(-4\) to show that all numbers less than \(-4\) are included in the solution.

Here's a representation of how the number line would look:

```
<---|----|----|----|----|----|----|----|----|----|---->
-6 -5 -4 -3 -2 -1 0 1 2 3

o
<==========
```

The open circle at \(-4\) indicates that \(-4\) is not part of the solution, and the shaded area to the left indicates all values less than \(-4\) are included in the solution.