Find the values of x which satisfy the inequality `-3 lt 2x -1 lt 19 ` .

Explanation

To solve the inequality \(-3 < 2x - 1 < 19\), we will break it down into two parts and solve it step by step.

### Step 1: Break the inequality into two parts
We have the compound inequality:
\[ -3 < 2x - 1 < 19 \]
This can be split into two separate inequalities:
1. \(-3 < 2x - 1\)
2. \(2x - 1 < 19\)

### Step 2: Solve the first part of the inequality
Starting with the first inequality:
\[ -3 < 2x - 1 \]
Add \(1\) to both sides:
\[ -3 + 1 < 2x \]
This simplifies to:
\[ -2 < 2x \]
Now, divide both sides by \(2\):
\[ -1 < x \]
This can be rewritten as:
\[ x > -1 \]

### Step 3: Solve the second part of the inequality
Now, we solve the second inequality:
\[ 2x - 1 < 19 \]
Add \(1\) to both sides:
\[ 2x < 19 + 1 \]
This simplifies to:
\[ 2x < 20 \]
Now, divide both sides by \(2\):
\[ x < 10 \]

### Step 4: Combine the results
From the two parts, we have:
\[ -1 < x < 10 \]
This means that \(x\) is in the open interval:
\[ x \in (-1, 10) \]

### Final Answer
The values of \(x\) that satisfy the inequality \(-3 < 2x - 1 < 19\) are:
\[ x \in (-1, 10) \]