Question

Solve the following inequality. Graph and check your solution.
negative StartFraction v Over 5 EndFraction greater than or equals 2.4
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Part 1
Solve the inequality.
  
enter your response here
​(Simplify your answer. Type an​ inequality.)

Answer 1

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:

1. 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.

2. 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.