Let's solve the inequality step by step:

Given inequality:
\[
1 - 9g \leq 9 - 7g
\]

### Step 1: Move the variable terms to one side
First, let's add \(7g\) to both sides to get rid of the \( -7g \) on the right-hand side:
\[
1 - 9g + 7g \leq 9 - 7g + 7g
\]
This simplifies to:
\[
1 - 2g \leq 9
\]

### Step 2: Move the constant term to the other side
Next, subtract 1 from both sides to move the constant term on the left-hand side:
\[
1 - 2g - 1 \leq 9 - 1
\]
This simplifies to:
\[
-2g \leq 8
\]

### Step 3: Solve for \(g\)
Now, divide both sides by \(-2\), and remember to flip the inequality sign because we are dividing by a negative number:
\[
g \geq \frac{8}{-2}
\]
This simplifies to:
\[
g \geq -4
\]

### Final Answer:
\[
g \geq -4
\]

Would you like more details on this solution?

Here are 5 related questions to deepen your understanding:
1. How do we solve linear inequalities with variables on both sides?
2. Why does the inequality sign flip when dividing by a negative number?
3. What are the similarities and differences between solving equations and inequalities?
4. Can this inequality have a graph representation on a number line?
5. How would the solution change if the inequality were strict (\(<\) instead of \(\leq\))?

**Tip:** Always check your inequality solution by plugging it back into the original inequality to verify.

Learn how to solve the linear inequality 1 - 9g ≤ 9 - 7g with a step-by-step solution. This problem covers key algebraic concepts like moving variable terms, flipping inequality signs, and solving for variables. Suitable for students in Grades 7-9.

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