Let's solve the given inequality step by step.

The inequality is:

$9 - x \geq 7$

Step 1: Isolate the variable $x$.

Subtract 9 from both sides to get rid of the constant on the left side:

$9 - x - 9 \geq 7 - 9$ $-x \geq -2$

Step 2: Solve for $x$.

To eliminate the negative sign in front of $x$, multiply both sides by $-1$. Remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign:

$x \leq 2$

Step 3: Express the solution in interval notation.

The solution $x \leq 2$ means that $x$ can take any value less than or equal to 2. In interval notation, this is written as:

$(-\infty, 2]$

This is the solution to the inequality.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide both sides of an inequality by a variable?
3. Can inequalities have multiple solutions?
4. How do you graph inequalities on a number line?
5. What is the difference between strict ($<$ or $>$) and non-strict inequalities ($\leq$ or $\geq$)?

Tip: Always remember to reverse the inequality sign when multiplying or dividing by a negative number!