Question

solve for f and graph the solution.
f + 4 < 14 - 9f or f - 15 + f > -3
plot the endpoints. select an endpoint to change it from closed to open. select
a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality \(f + 4<14 - 9f\)

Add \(9f\) to both sides:
\(f+9f + 4<14-9f + 9f\)
\(10f+4<14\)
Subtract \(4\) from both sides:
\(10f+4 - 4<14 - 4\)
\(10f<10\)
Divide both sides by \(10\):
\(f < 1\)

Step2: Solve the second inequality \(f-15 + f>-3\)

Combine like - terms:
\(2f-15>-3\)
Add \(15\) to both sides:
\(2f-15 + 15>-3 + 15\)
\(2f>12\)
Divide both sides by \(2\):
\(f>6\)

Answer:

The solution of the compound inequality \(f + 4<14 - 9f\) or \(f-15 + f>-3\) is \(f < 1\) or \(f>6\). On the number - line, for \(f < 1\), we have an open circle at \(f = 1\) and a ray pointing to the left. For \(f>6\), we have an open circle at \(f = 6\) and a ray pointing to the right.