Question

solve the inequality and graph the solution.
r + 7 < 10
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Isolate the variable \( r \)

Subtract \( 7 \) from both sides of the inequality \( r + 7<10 \).
Using the subtraction property of inequalities: \( r+7 - 7<10 - 7 \).

Step2: Simplify the inequality

Simplify both sides. On the left - hand side, \( r+7 - 7=r \), and on the right - hand side, \( 10 - 7 = 3 \). So the inequality becomes \( r<3 \).

To graph \( r < 3 \):

• The endpoint is at \( r = 3 \). Since the inequality is \( < \) (not \( \leq \)), the endpoint at \( r = 3 \) is open (a hollow circle).
• The solution set includes all real numbers less than \( 3 \), so we draw a ray to the left of \( 3 \) on the number line.

Answer:

The solution of the inequality \( r + 7<10 \) is \( r<3 \). On the number line, there is an open circle at \( 3 \) and a ray extending to the left of \( 3 \).