We can solve the inequality step by step.

Given:
\[
7(2 - x) + 9 < 2
\]

### Step 1: Expand the terms.
\[
7 \times 2 - 7 \times x + 9 < 2
\]
This simplifies to:
\[
14 - 7x + 9 < 2
\]

### Step 2: Combine like terms.
\[
23 - 7x < 2
\]

### Step 3: Isolate the variable term.
Subtract 23 from both sides:
\[
-7x < 2 - 23
\]
\[
-7x < -21
\]

### Step 4: Solve for \( x \).
Divide both sides by -7, and **remember to reverse the inequality sign** when dividing by a negative number:
\[
x > \frac{-21}{-7}
\]
\[
x > 3
\]

### Final Answer:
\[
x > 3
\]

Would you like further details on this solution?

Here are 5 related questions you could explore:
1. What would the solution be if the inequality was \( 7(2-x) + 9 \leq 2 \)?
2. How would you solve \( 5(3-x) + 8 > 10 \)?
3. What happens if we reverse the inequality, \( 7(2 - x) + 9 > 2 \)?
4. How can we represent the solution \( x > 3 \) on a number line?
5. How would the solution change if it was \( 7(2 + x) + 9 < 2 \)?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Learn how to solve the inequality 7(2 - x) + 9 < 2 using key algebraic concepts like the distributive property and properties of inequalities. This step-by-step guide covers simplifying expressions and solving linear inequalities. Suitable for students in Grades 7-9.

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