`{x : 4-2x gt -6, x in Z}`

Answer

To solve the inequality \(4 - 2x > -6\) where \(x\) is an integer, we will follow these steps:

### Step 1: Rewrite the inequality
Start with the original inequality:
\[ 4 - 2x > -6 \]

### Step 2: Move terms around
Add \(2x\) to both sides of the inequality to isolate the variable on one side:
\[ 4 > -6 + 2x \]

### Step 3: Simplify the right side
Now, add \(6\) to both sides:
\[ 4 + 6 > 2x \]
This simplifies to:
\[ 10 > 2x \]

### Step 4: Divide by 2
Now, divide both sides by \(2\) to solve for \(x\):
\[ 5 > x \]
or equivalently,
\[ x < 5 \]

### Step 5: Identify the set of integers
Since \(x\) must be an integer, the integers that satisfy \(x < 5\) are:
\[ \{..., -3, -2, -1, 0, 1, 2, 3, 4\} \]

### Final Set
Thus, the set of integers \(x\) that satisfy the inequality \(4 - 2x > -6\) is:
\[ \{x \in \mathbb{Z} : x < 5\} = \{..., -3, -2, -1, 0, 1, 2, 3, 4\} \]