Question

Which values are solutions to the inequality?

​ ​5r≤6r−8​ ​

Select each correct answer.

Responses

r = 7
r = 7

r = 8
r = 8

r = 9
r = 9

r = 10
r = 10

Answer 1

To solve the inequality \( 5r \leq 6r - 8 \), we can start by isolating \( r \):

1. Subtract \( 6r \) from both sides:
\[
5r - 6r \leq -8
\]
This simplifies to:
\[
-r \leq -8
\]

2. Now, to solve for \( r \), multiply both sides by -1. Remember to reverse the inequality sign when multiplying by a negative number:
\[
r \geq 8
\]

Now that we have the solution \( r \geq 8 \), we can evaluate the provided options:

- **r = 7**: Not a solution (7 < 8)
- **r = 8**: Solution (8 = 8)
- **r = 9**: Solution (9 > 8)
- **r = 10**: Solution (10 > 8)

Thus, the correct responses are:
- \( r = 8 \)
- \( r = 9 \)
- \( r = 10 \)