If `x in{-2,-1,0,1,2,3,4,5}`, find the solution set of each of the following inequations : `3x+4lt15`

Answer

To solve the inequality \(3x + 4 < 15\) for \(x\) belonging to 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:
\[ 3x + 4 < 15 \]

### Step 2: Isolate the Term with \(x\)
Subtract 4 from both sides:
\[ 3x < 15 - 4 \]
\[ 3x < 11 \]

### Step 3: Solve for \(x\)
Now, divide both sides by 3:
\[ x < \frac{11}{3} \]
Calculating \(\frac{11}{3}\) gives approximately \(3.67\).

### Step 4: Identify Values from the Set
Now we need to find all values of \(x\) from the set \(\{-2, -1, 0, 1, 2, 3, 4, 5\}\) that are less than \(3.67\).

The values from the set that are less than \(3.67\) are:
\[ -2, -1, 0, 1, 2, 3 \]

### Step 5: Write the Solution Set
Thus, the solution set for the inequality \(3x + 4 < 15\) is:
\[ \{-2, -1, 0, 1, 2, 3\} \]

---