If `x in{-2,-1,0,1,2,3,4,5}`, find the solution set of each of the following inequations : `2xgt5`

Answer

To solve the inequality \(2x > 5\) for \(x\) in the set \{-2, -1, 0, 1, 2, 3, 4, 5\}, follow these steps:

### Step 1: Solve the Inequality
Start with the inequality:
\[ 2x > 5 \]
To isolate \(x\), divide both sides by 2:
\[ x > \frac{5}{2} \]
Calculating \(\frac{5}{2}\):
\[ \frac{5}{2} = 2.5 \]
So, we have:
\[ x > 2.5 \]

### Step 2: Identify the Values of \(x\)
Now, we need to find which values of \(x\) from the set \{-2, -1, 0, 1, 2, 3, 4, 5\} satisfy the inequality \(x > 2.5\).

### Step 3: Check Each Value
- For \(x = -2\): \(-2\) is not greater than \(2.5\).
- For \(x = -1\): \(-1\) is not greater than \(2.5\).
- For \(x = 0\): \(0\) is not greater than \(2.5\).
- For \(x = 1\): \(1\) is not greater than \(2.5\).
- For \(x = 2\): \(2\) is not greater than \(2.5\).
- For \(x = 3\): \(3\) is greater than \(2.5\).
- For \(x = 4\): \(4\) is greater than \(2.5\).
- For \(x = 5\): \(5\) is greater than \(2.5\).

### Step 4: Compile the Solution Set
The values of \(x\) that satisfy the inequality \(x > 2.5\) are \(3\), \(4\), and \(5\).

Thus, the solution set is:
\[ \{3, 4, 5\} \]

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