Solving the inequality:

The inequality is:

$9 - 4x \geq 37$

Step 1: Isolate the variable term Subtract 9 from both sides: $9 - 4x - 9 \geq 37 - 9$ $-4x \geq 28$

Step 2: Solve for $x$ Divide both sides by $-4$. Remember to reverse the inequality when dividing by a negative number: $x \leq \frac{28}{-4}$ $x \leq -7$

Final Solution:

$x \leq -7$

Graphing the Solution:

To represent $x \leq -7$ on a number line:

1. Draw a number line.
2. Place a closed circle at $-7$ (because the inequality includes equality, $\leq$).
3. Shade all values to the left of $-7$ to represent that $x$ is less than or equal to $-7$.

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Let me know if you'd like me to create a detailed graph or clarify further steps!

5 Related Questions:

1. How do you graph strict inequalities like $x < -7$ on a number line?
2. What changes when you multiply or divide by a negative number in an inequality?
3. Can you explain why the inequality sign flips when dividing by a negative number?
4. How would you represent $x \geq 7$ on a number line instead?
5. What are some real-world scenarios where solving inequalities is applied?

Tip:

Always double-check your inequality's direction after dividing by a negative number, as this is a common mistake.