Question

create a number line for the solution 4x-36<-12

Answer 1

To solve the inequality \(4x - 36 < -12\), you first need to isolate \(x\). Here’s how to do that step-by-step:

1. **Add 36 to both sides:**
\[
4x - 36 + 36 < -12 + 36
\]
\[
4x < 24
\]

2. **Divide both sides by 4:**
\[
x < \frac{24}{4}
\]
\[
x < 6
\]

Now, you have the solution \(x < 6\).

### Creating a Number Line

To represent this inequality on a number line:

1. Draw a horizontal line.
2. Mark a point at \(6\) with an open circle, indicating that \(6\) is not included in the solution (because the inequality is strict, \(<\)).
3. Shade to the left of \(6\) to represent all numbers less than \(6\).

Here's a simple representation of a number line:

```
<---|---|---|---|---|---|---|---|---|---|--->
3 4 5 6 7 8 ... (continue as needed)
o-----------------------> (Shade to the left)
```

- The **open circle** at \(6\) indicates that \(6\) is not included in the solution, and the shaded line to the left shows the values that satisfy \(x < 6\).