Exercise 48 Page 164

We are given two inequalities. n/3 ≥ - 4 and n/- 5 ≥ 1 We will solve and graph one inequality at a time. Let's start with the first one. n/3 ≥ - 4 To solve the inequality, we will use the Multiplication Property of Inequality.

We can multiply both sides of the inequality by 3, and the inequality will remain true. That is because 3 is a positive number.

The solution of the first inequality is all numbers greater than or equal to - 12. Let's graph it! First we will draw a number line. Then, we will mark - 12 on it. We will use a closed circle, because - 12 is a solution.

We will choose a test point to check which side of the number line we should shade. We can take n = - 11. - 11 ≥ - 12 ✓ We can see that n = - 11 is the solution of the inequality. Therefore, we will shade the right side of the number line.

Next, we will solve the second inequality. n/- 5 ≥ 1 This time we will multiply both sides of the inequality by a negative number. Let's consider the second case of the Multiplication Property of Inequality.

Let's multiply both sides of the inequality by - 5. We will also reverse the inequality symbol, because - 5 is a negative number.

The solution of the second inequality is all numbers less than or equal to - 5. To graph the inequality n ≤ - 5, we will graph a number line. We will use a closed circle to mark - 5, because - 5 is the solution.

We will choose a test point to check which side of the number line we should shade. We can take n = - 6. - 6 ≤ - 5 ✓ We can see that n = - 6 is the solution of the inequality. Therefore, we will shade the left side of the number line.

The solutions that satisfies both inequalities are all numbers greater than or equal to - 12 and less than or equal to - 5. To graph it, we will shade the region on the number line that is between - 12 and - 5.