Here is the breakdown and solution for each question from the uploaded image:

Question 1:

"If -3 + n ≤ 25, which inequality represents the possible range of values for 4n - 12?"

1. Solve for $n$: $-3 + n \leq 25 \implies n \leq 28$
2. Substitute $n \leq 28$ into $4n - 12$: $4n - 12 \leq 4(28) - 12 = 100$ Thus, $4n - 12 \leq 100$.

Answer: B) 4n - 12 ≤ 100

Question 2:

"Which of the following numbers is NOT a solution to the inequality $\frac{1}{2} x - \frac{7}{9} \leq \frac{5}{2}$?"

1. Simplify inequality: $\frac{1}{2}x \leq \frac{5}{2} + \frac{7}{9}$ Convert to common denominator: $\frac{7}{9} = \frac{14}{18}, \quad \frac{5}{2} = \frac{45}{18} \implies \frac{5}{2} + \frac{7}{9} = \frac{59}{18}$ $\frac{1}{2}x \leq \frac{59}{18} \implies x \leq \frac{59}{18} \times 2 = \frac{59}{9}$
2. Evaluate each number: $\frac{59}{9} \approx 6.56$ Numbers greater than $6.56$ are NOT solutions. $16$ does not satisfy this.

Answer: A) 16

Question 3:

"If -3a + 7 ≤ 5a − 17, what is the greatest possible value of $3a + 7$?"

1. Simplify inequality: $-3a + 7 \leq 5a - 17 \implies 8a \geq 24 \implies a \geq 3$
2. Find $3a + 7$ for $a = 3$: $3(3) + 7 = 16$

Answer: A) 16

Question 4:

"Nine is not more than the sum of a number and 17."

1. Convert to inequality: $9 \leq n + 17$
2. Simplify: $n \geq -8$

Answer: D) 9 ≤ n + 17

Question 5:

"The product of 7 and number $n$ is no less than 91."

1. Convert to inequality: $7n \geq 91$
2. Simplify: $n \geq 13$

Answer: C) 7n ≥ 91

Question 6:

"Which of the following inequalities represents the graph above?"

1. Analyze graph: $n \leq -5$.

Answer: A) n ≤ -5

Would you like detailed steps for any of the questions above? Here are 5 related questions to expand your understanding:

1. How do we convert verbal statements into inequalities systematically?
2. Can you explain the relationship between inequalities and their graphs?
3. What are strategies for solving compound inequalities?
4. How can we verify a solution satisfies an inequality?
5. What methods can simplify inequalities involving fractions?

Tip: Always isolate the variable step by step to maintain accuracy in solving inequalities.