Answer :
Answer:
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Explanation:
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Answer:
Explanation:
To solve the compound inequality \(-1 \leq 3 + 4x < 23\), we need to break it down into two separate inequalities and solve them individually:
1. \(-1 \leq 3 + 4x\)
2. \(3 + 4x < 23\)
### Solving \(-1 \leq 3 + 4x\)
Subtract 3 from both sides:
\[
-1 - 3 \leq 4x
\]
\[
-4 \leq 4x
\]
Divide both sides by 4:
\[
\frac{-4}{4} \leq x
\]
\[
-1 \leq x
\]
### Solving \(3 + 4x < 23\)
Subtract 3 from both sides:
\[
4x < 23 - 3
\]
\[
4x < 20
\]
Divide both sides by 4:
\[
x < \frac{20}{4}
\]
\[
x < 5
\]
### Combining the two inequalities
We combine the results of both inequalities:
\[
-1 \leq x < 5
\]
### Representing the solution set on the number line
To represent the solution set \(-1 \leq x < 5\) on the number line:
- Draw a number line.
- Mark the points \(-1\) and \(5\).
- Draw a closed circle at \(-1\) to indicate that \(-1\) is included in the solution set.
- Draw an open circle at \(5\) to indicate that \(5\) is not included in the solution set.
- Shade the region between \(-1\) and \(5\) to indicate all the numbers in that interval are included.
The number line representation looks like this:
```
---|------------------|------------------
-1 5
[==================)
```
The solution set is \([-1, 5)\).