Question

Solve each compound inequality and graph its solution. < 2 and 3r > 3

Answer 1

Solve 3r > 3 by dividing by 3 to get r > 1, and graph it with an open circle at 1 and shading to the right. The first inequality is incomplete and cannot be solved without additional information.

Step-by-step explanation:

To solve the compound inequality < 2 and 3r > 3, we need to treat each inequality separately. First, the expression with the missing variable cannot be solved as is because it is not a complete inequality. Assuming there is a typo, let's address the valid inequality. Divide both sides of the second inequality by 3 to isolate r:

3r > 3

r > 1

Now, to graph this inequality, you draw a number line, and a plot point at r = 1. Since the inequality is > (greater than) and not ≥ (greater than or equal to), you use an open circle to indicate that 1 is not included in the solution. Then, you shade the number line to the right of 1 to show all the numbers greater than 1.

For the first inequality that lacks a variable or further context, you would typically graph r < 2 using a similar approach: an open circle at 2 and shading to the left if 'r' is assumed to be the variable in question.