Which values are solutions to the inequality?

Question

​ ​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:

• \( r = 8 \)
• \( r = 9 \)
• \( r = 10 \)