If the replacement set is the set of integers, (I or Z), between - 6 and 8, find the solution set of :
`15 - 3x gt x - 3`.

Answer

To solve the inequality \( 15 - 3x > x - 3 \) with the replacement set being the integers between -6 and 8, we will follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ 15 - 3x > x - 3 \]

### Step 2: Move all terms involving \( x \) to one side
Add \( 3x \) to both sides of the inequality:
\[ 15 > x + 3x - 3 \]
This simplifies to:
\[ 15 > 4x - 3 \]

### Step 3: Isolate the term with \( x \)
Next, add 3 to both sides:
\[ 15 + 3 > 4x \]
This simplifies to:
\[ 18 > 4x \]

### Step 4: Solve for \( x \)
Now, divide both sides by 4:
\[ \frac{18}{4} > x \]
This simplifies to:
\[ 4.5 > x \quad \text{or} \quad x < 4.5 \]

### Step 5: Identify the replacement set
The replacement set consists of integers between -6 and 8, which are:
\[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 \]

### Step 6: Determine the solution set
Since \( x \) must be less than 4.5, we consider the integers from the replacement set that are less than 4.5:
\[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 \]

### Final Solution Set
Thus, the solution set is:
\[ \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4\} \]

---