Solve for f.

Question

9>f–8>2
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 9 > f - 8 > 2 \), we can break it down into two separate inequalities:

1. \( 9 > f - 8 \)
2. \( f - 8 > 2 \)

Now, solve each inequality:

First inequality: \[ 9 > f - 8 \] Add 8 to both sides: \[ 9 + 8 > f \] \[ 17 > f \quad \text{or} \quad f < 17 \]

Second inequality: \[ f - 8 > 2 \] Add 8 to both sides: \[ f > 2 + 8 \] \[ f > 10 \]

Now, combining both results, we get: \[ 10 < f < 17 \]

Thus, the solution in the form of a compound inequality is: \[ 10 < f < 17 \]

This means that \( f \) can take any integer value from 11 to 16.