Question

Solve the inequality. Graph and check your solution.
negative four fifths m less than minus 4
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Part 1
m
▼
greater than or equals
less than or equals
greater than
less than
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the inequality \(-\frac{4}{5}m < -4\), follow these steps:

1. **Isolate \(m\)**:
To isolate \(m\), divide both sides of the inequality by \(-\frac{4}{5}\). Remember that when you divide an inequality by a negative number, you must flip the inequality sign.

\[
m > \frac{-4}{-\frac{4}{5}}
\]

2. **Simplify the right side**:
Dividing by a fraction is the same as multiplying by its reciprocal. So, we simplify:

\[
m > -4 \times -\frac{5}{4}
\]

This simplifies to:

\[
m > 5
\]

### Solution

So, the solution to the inequality is:

\[
m > 5
\]

### Graph the solution

To graph the solution \(m > 5\):

- Draw a number line.
- Place an open circle at the point \(5\) to indicate that \(5\) is not included in the solution (since it's "greater than").
- Shade the line to the right of \(5\) to indicate all values greater than \(5\) satisfy the inequality.

### Check the solution

Let's check a value greater than \(5\), for example, \(m = 6\):

Substitute \(m = 6\) back into the original inequality:

\[
-\frac{4}{5}(6) < -4
\]

Calculating the left side:

\[
-\frac{24}{5} < -4
\]

Now, convert \(-4\) to a fraction with a denominator of \(5\):

\[
-4 = -\frac{20}{5}
\]

Now we have:

\[
-\frac{24}{5} < -\frac{20}{5}
\]

Since \(-24 < -20\) is true, our solution \(m > 5\) is correct.

### Summary

The solution to the inequality is:

\[
m > 5
\]

You can graph this on a number line as described and confirm the solution by substituting a value greater than \(5\).