Answer:
[tex]\{r | r \ge -3 \}[/tex]
Step-by-step explanation:
[tex] 7 - 9r - (r + 12) \le 25 [/tex]
Remember that to deal with the negative sign to the left of the parentheses, you must think of it as a -1 multiplying the parentheses, and you distribute the -1 by multiply each term inside the parentheses by -1. That changes all the signs inside the parentheses.
[tex] 7 - 9r - r - 12 \le 25 [/tex]
Combine like terms on the left side.
[tex] -10r - 5 \le 25 [/tex]
Add 5 to both sides.
[tex] -10r \le 30 [/tex]
We now divide both sides by -10. Remember that when you divide both sides fo an inequality by a negative number, the inequality sign changes direction.
[tex] r \ge -3 [/tex]
Answer: [tex]\{r | r \ge -3 \}[/tex]
