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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!

Solve the linear inequality: 9 - x ≥ 7. Express the solution using interval notation.

Learn how to solve the linear inequality 9 - x ≥ 7 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality manipulation and reversing the inequality when multiplying by a negative number. Suitable for students in Grades 7-9.

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