If `x in{-2,-1,0,1,2,3,4,5}`, find the solution set of each of the following inequations : `7-xgt0`

Answer

To solve the inequality \( 7 - x > 0 \) given that \( x \) can take values from the set \{-2, -1, 0, 1, 2, 3, 4, 5\}, we will follow these steps:

### Step 1: Rewrite the Inequality
Start with the inequality:
\[ 7 - x > 0 \]

### Step 2: Isolate \( x \)
To isolate \( x \), we can rearrange the inequality:
\[ 7 > x \]
This can also be written as:
\[ x < 7 \]

### Step 3: Identify the Values of \( x \)
Now, we need to check which values from the set \{-2, -1, 0, 1, 2, 3, 4, 5\} satisfy the inequality \( x < 7 \).

### Step 4: Check Each Value
- For \( x = -2 \): \(-2 < 7\) (True)
- For \( x = -1 \): \(-1 < 7\) (True)
- For \( x = 0 \): \(0 < 7\) (True)
- For \( x = 1 \): \(1 < 7\) (True)
- For \( x = 2 \): \(2 < 7\) (True)
- For \( x = 3 \): \(3 < 7\) (True)
- For \( x = 4 \): \(4 < 7\) (True)
- For \( x = 5 \): \(5 < 7\) (True)

### Step 5: Compile the Solution Set
Since all the values from the set satisfy the inequality \( x < 7 \), the solution set is:
\[ \{-2, -1, 0, 1, 2, 3, 4, 5\} \]

### Final Answer
The solution set for the inequality \( 7 - x > 0 \) is:
\[ \{-2, -1, 0, 1, 2, 3, 4, 5\} \]