To solve the inequality \(-\frac{2}{5}m > -2\), follow these steps:
- Solve for \(m\) by isolating it on one side of the inequality. Begin by multiplying both sides of the inequality by \(-\frac{5}{2}\). Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.
\[ -\frac{2}{5}m > -2 \]
Multiply both sides by \(-\frac{5}{2}\):
\[ m < -2 \cdot -\frac{5}{2} \]
- Calculate the right side:
\[ m < 5 \]
The solution to the inequality is:
\[ m < 5 \]
Graphing the Solution
To graph this solution on a number line:
- Draw a number line.
- Place an open circle on \(5\) to indicate that \(5\) is not included in the solution.
- Shade to the left of \(5\) to represent all values less than \(5\).
Checking the Solution
To check if our solution is correct, we can test a number less than \(5\) (e.g., \(m = 0\)):
Plug \(m = 0\) into the original inequality:
\[ -\frac{2}{5}(0) > -2 \] \[ 0 > -2 \quad \text{(true)} \]
Now, test a number greater than \(5\) (e.g., \(m = 6\)):
\[ -\frac{2}{5}(6) > -2 \] \[ -\frac{12}{5} > -2 \quad \text{(false)} \]
This confirms that our solution \(m < 5\) is correct.
Final Answer:
The final answer is:
\[ m < 5 \]