Question

4m - 5 > 7 or 4m - 5 < 9

Answer 1

To solve the inequalities \(4m - 5 > 7\) and \(4m - 5 < 9\), we can tackle each one separately.

1. Solving the inequality \(4m - 5 > 7\):

\[
4m - 5 > 7
\]
Add 5 to both sides:
\[
4m > 12
\]
Divide both sides by 4:
\[
m > 3
\]

2. Solving the inequality \(4m - 5 < 9\):

\[
4m - 5 < 9
\]
Add 5 to both sides:
\[
4m < 14
\]
Divide both sides by 4:
\[
m < 3.5
\]

Now, we combine the results from both inequalities:

- From the first inequality, we have \(m > 3\).
- From the second inequality, we have \(m < 3.5\).

Thus, the solution to the compound inequality \(4m - 5 > 7\) or \(4m - 5 < 9\) is:

\[
3 < m < 3.5
\]

This means \(m\) can take any value in the range \( (3, 3.5) \).