Question

Solve the compound inequality.
5 - m < 4 or 7m > 35

Answer 1

To solve the compound inequality \(5 - m < 4\) or \(7m > 35\), we will solve each part separately.

1. Solve \(5 - m < 4\):

\[
5 - m < 4
\]
Subtract 5 from both sides:
\[
-m < 4 - 5
\]
\[
-m < -1
\]
Multiply both sides by -1 (remember to flip the inequality sign):
\[
m > 1
\]

2. Solve \(7m > 35\):

\[
7m > 35
\]
Divide both sides by 7:
\[
m > 5
\]

Now we combine the results of both inequalities:

- From \(5 - m < 4\), we have \(m > 1\).
- From \(7m > 35\), we have \(m > 5\).

Since the compound inequality is connected by "or", the solution is the union of the two sets:

The solution to the compound inequality \(5 - m < 4\) or \(7m > 35\) is:

\[
m > 1
\]

So, the final answer is:

\[
m > 1
\] (This includes all values greater than 1.)