Solve for f.

Question

5f–6<14 or f+10≥17
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequalities \( 5f - 6 < 14 \) and \( f + 10 \geq 17 \), we will solve each inequality separately.

For the first inequality:

1. Start with the inequality: \[ 5f - 6 < 14 \]

2. Add 6 to both sides: \[ 5f < 20 \]

3. Divide both sides by 5: \[ f < 4 \]

For the second inequality:

1. Start with the inequality: \[ f + 10 \geq 17 \]

2. Subtract 10 from both sides: \[ f \geq 7 \]

Combine the results:

The solution to the compound inequality is: \[ f < 4 \quad \text{or} \quad f \geq 7 \]

In interval notation, this can be expressed as: \[ (-\infty, 4) \cup [7, \infty) \]

As a result, the integers that satisfy the inequalities are all integers less than 4 or greater than or equal to 7. Thus, the integer solution can be represented as: \[ { \ldots, -2, -1, 0, 1, 2, 3 } \cup { 7, 8, 9, 10, \ldots } \]

In summary, the solution in a concise form is: \[ f < 4 \quad \text{or} \quad f \geq 7 \]