If `x inZ^(-)`, find the solution set of each of the following inequations : `-29lt9x-2`

Answer

To solve the inequality \(-29 < 9x - 2\) where \(x\) belongs to the set of negative integers (\(Z^-\)), we will follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ -29 < 9x - 2 \]

### Step 2: Isolate the term with \(x\)
Add 2 to both sides of the inequality to isolate the term with \(x\):
\[ -29 + 2 < 9x \]
This simplifies to:
\[ -27 < 9x \]

### Step 3: Divide by 9
Next, divide both sides of the inequality by 9. Remember that since we are dividing by a positive number, the direction of the inequality remains the same:
\[ \frac{-27}{9} < x \]
This simplifies to:
\[ -3 < x \]
or equivalently,
\[ x > -3 \]

### Step 4: Consider the set of negative integers
Since we are looking for solutions where \(x\) belongs to the set of negative integers (\(Z^-\)), we need to find the negative integers that are greater than \(-3\).

### Step 5: Identify the solution set
The negative integers greater than \(-3\) are:
- \(-2\)
- \(-1\)

Thus, the solution set is:
\[ \{ -2, -1 \} \]

### Final Answer
The solution set for the inequality \(-29 < 9x - 2\) where \(x\) belongs to negative integers is:
\[ \{ -2, -1 \} \]

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