If `x in{-2,-1,0,1,2,3,4,5}`, find the solution set of each of the following inequations : `3-12xgt-21`

Answer

To solve the inequality \(3 - 12x > -21\) 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 original inequality:
\[ 3 - 12x > -21 \]

### Step 2: Isolate the term with \(x\)
To isolate the term with \(x\), we will first add \(21\) to both sides of the inequality:
\[ 3 + 21 - 12x > 0 \]
This simplifies to:
\[ 24 - 12x > 0 \]

### Step 3: Rearrange the Inequality
Now, we will rearrange the inequality to isolate \(x\):
\[ 24 > 12x \]
or equivalently,
\[ 12x < 24 \]

### Step 4: Divide by 12
Next, we divide both sides of the inequality by \(12\):
\[ x < 2 \]

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

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

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