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

Answer

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

### Step 1: Rewrite the Inequality
Start with the original inequality:
\[ 3 - 4x > -2 \]

### Step 2: Isolate the Variable
Add \(2\) to both sides of the inequality to isolate the term involving \(x\):
\[ 3 + 2 > 4x \]
This simplifies to:
\[ 5 > 4x \]

### Step 3: Divide by 4
Now, divide both sides by \(4\) to solve for \(x\):
\[ \frac{5}{4} > x \]
This can also be written as:
\[ x < \frac{5}{4} \]

### Step 4: Convert \(\frac{5}{4}\) to Decimal
Convert \(\frac{5}{4}\) to a decimal for easier comparison:
\[ \frac{5}{4} = 1.25 \]

### Step 5: Identify the Solution Set
Now, we need to find the values of \(x\) from the given set \(\{-2, -1, 0, 1, 2, 3, 4, 5\}\) that are less than \(1.25\). The values that satisfy this condition are:
\(-2, -1, 0, 1\).

### Step 6: Write the Final Solution Set
Thus, the solution set for the inequality \(3 - 4x > -2\) is:
\[ \{-2, -1, 0, 1\} \]