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 \( (3, 3.5) \).