If `x in{-2,-1,0,1,2,3,4,5}`, find the solution set of each of the following inequations : `3x-8lt1`

Answer

To solve the inequality \(3x - 8 < 1\) for \(x\) in the set \{-2, -1, 0, 1, 2, 3, 4, 5\}, we will follow these steps:

### Step 1: Rewrite the Inequality
Start with the given inequality:
\[ 3x - 8 < 1 \]

### Step 2: Add 8 to Both Sides
To isolate the term with \(x\), add 8 to both sides of the inequality:
\[ 3x - 8 + 8 < 1 + 8 \]
This simplifies to:
\[ 3x < 9 \]

### Step 3: Divide by 3
Next, divide both sides by 3 to solve for \(x\):
\[ \frac{3x}{3} < \frac{9}{3} \]
This simplifies to:
\[ x < 3 \]

### Step 4: 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 satisfy the condition \(x < 3\). The values that satisfy this condition are:
\[ \{-2, -1, 0, 1, 2\} \]

### Final Solution Set
Thus, the solution set for the inequality \(3x - 8 < 1\) is:
\[ \{x \in \{-2, -1, 0, 1, 2\} \} \]

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