Question

do not break it up when solving -51 is less than or equal to 5x-1 is less than 4 solve give solution and graph

Answer 1

To solve the compound inequality \(-51 \leq 5x - 1 < 4\) without breaking it up, you can treat it as one entire inequality. We will solve it step by step.

1. **Solve the left side of the inequality:**
\[
-51 \leq 5x - 1
\]
Add 1 to both sides:
\[
-51 + 1 \leq 5x
\]
\[
-50 \leq 5x
\]
Divide by 5:
\[
-10 \leq x \quad \text{or} \quad x \geq -10
\]

2. **Solve the right side of the inequality:**
\[
5x - 1 < 4
\]
Add 1 to both sides:
\[
5x < 4 + 1
\]
\[
5x < 5
\]
Divide by 5:
\[
x < 1
\]

3. **Combine the results:**
From the two parts, we have:
\[
-10 \leq x < 1
\]
Therefore, the solution to the compound inequality is:
\[
-10 \leq x < 1
\]

4. **Graph the solution:**
To graph the solution on the number line:
- Draw a line with numbers from -10 to 1.
- Place a closed dot at -10 (indicating -10 is included).
- Place an open dot at 1 (indicating 1 is not included).
- Shade the region between -10 and 1.

Here's a representation of the graph:

```
<-----●==================○----->
-10 1
```

### Final Result:
The solution to the inequality \(-51 \leq 5x - 1 < 4\) is:
\[
x \in [-10, 1)
\]