To solve the inequality
\[ -\frac{v}{5} \geq 2.4, \]
you can start by multiplying both sides of the inequality by -5. Remember that when you multiply or divide by a negative number, the direction of the inequality sign must be reversed. Therefore, we have:
\[ v \leq -12. \]
Thus, the solution to the inequality is
\[ v \leq -12. \]
Graphing the Solution
To graph this solution on a number line:
- Draw a number line.
- Locate -12 on the number line.
- Since the inequality is "less than or equal to," draw a solid circle at -12 to indicate that -12 is included in the solution.
- Shade everything to the left of -12 to indicate all numbers less than -12 are included in the solution.
Checking the Solution
To check the solution:
-
Pick a number less than or equal to -12 (for example, -12). \[ -\frac{-12}{5} = \frac{12}{5} = 2.4. \] Since \( 2.4 \geq 2.4 \) is true, -12 is a valid solution.
-
Pick a number greater than -12 (for example, -11). \[ -\frac{-11}{5} = \frac{11}{5} = 2.2. \] Since \( 2.2 \geq 2.4 \) is false, -11 is not a valid solution.
Thus, the solution \( v \leq -12 \) is confirmed to be correct.