Exercise 50 Page 164

We are given two inequalities. - 1/2s > - 7 and 1/3s < 12 We will solve and graph one inequality at a time. Let's start with the first one. - 1/2s > - 7 To solve the inequality, we will use the Multiplication Property of Inequality.

Let's multiply both sides of the inequality by - 2. We will also reverse the inequality symbol, because - 2 is a negative number.

The solution of the first inequality is all numbers less than 14. Let's graph it! First we will draw a number line. Then, we will mark 14 on it. We will use an open circle, because 14 is not a solution.

We will choose a test point to check which side of the number line we should shade. We can take s = 13. 13 < 14 ✓ We can see that s = 13 is the solution of the inequality. Therefore, we will shade the left side of the number line.

Next, we will solve the second inequality. 1/3s < 12 This time we will multiply both sides of the inequality by a positive number. Let's consider the first case of the Multiplication Property of Inequality.

Let's multiply both sides of the inequality by 3. The inequality will remain true, because 3 is a positive number.

The solution of the second inequality is all numbers less than 36. To graph the inequality s < 36, we will graph a number line. We will use an open circle to mark 36, because 36 is not a solution.

We will choose a test point to check which side of the number line we should shade. We can take s = 35. 35 < 36 ✓ We can see that s = 35 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 less than 14 and less than 36. This means that the solutions are less than 14. To graph it, we will shade the region on the number line that is to the left from 14.