To solve the inequality \( 4v \geq 9v - 40 \), let's follow these steps:

### Step 1: Move all terms involving \( v \) to one side.
Subtract \( 9v \) from both sides of the inequality:

\[
4v - 9v \geq -40
\]

### Step 2: Simplify the expression.
\[
-5v \geq -40
\]

### Step 3: Solve for \( v \).
Divide both sides by \( -5 \), and remember to **reverse the inequality** sign when dividing by a negative number:

\[
v \leq \frac{-40}{-5}
\]

\[
v \leq 8
\]

### Final solution:
\[
v \leq 8
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Solve the inequality \( 6v + 3 \geq 2v + 15 \).
2. Solve \( -7v \leq 3v + 21 \).
3. What is the solution for \( 5v - 10 \geq 3v + 8 \)?
4. Solve \( 2(4v - 5) \leq 6v + 8 \).
5. Solve the inequality \( 12 - 3v \geq 2v \).

**Tip:** Always reverse the inequality when multiplying or dividing by a negative number.

Discover how to solve the linear inequality 4v ≥ 9v − 40 with a step-by-step guide. This solution includes key algebra concepts, such as moving terms and reversing inequalities when dividing by negative numbers. Perfect for students in Grades 7-9.

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