Let's solve each inequality step-by-step:
### Problem 9: [tex]\( 2b + 3 > 15 \)[/tex]
1. Subtract 3 from both sides:
[tex]\[ 2b + 3 - 3 > 15 - 3 \][/tex]
[tex]\[ 2b > 12 \][/tex]
2. Divide both sides by 2:
[tex]\[ \frac{2b}{2} > \frac{12}{2} \][/tex]
[tex]\[ b > 6 \][/tex]
So, the solution for Problem 9 is:
[tex]\[ b > 6 \][/tex]
---
### Problem 11: [tex]\( 6r - 18 \geq 36 \)[/tex]
1. Add 18 to both sides:
[tex]\[ 6r - 18 + 18 \geq 36 + 18 \][/tex]
[tex]\[ 6r \geq 54 \][/tex]
2. Divide both sides by 6:
[tex]\[ \frac{6r}{6} \geq \frac{54}{6} \][/tex]
[tex]\[ r \geq 9 \][/tex]
So, the solution for Problem 11 is:
[tex]\[ r \geq 9 \][/tex]
---
### Problem 13: [tex]\( \frac{3}{2}e - 34 < -36 \)[/tex]
1. Add 34 to both sides:
[tex]\[ \frac{3}{2}e - 34 + 34 < -36 + 34 \][/tex]
[tex]\[ \frac{3}{2}e < -2 \][/tex]
2. Multiply both sides by [tex]\(\frac{2}{3}\)[/tex] to solve for [tex]\(e\)[/tex]:
[tex]\[ \left(\frac{3}{2}e\right) \cdot \frac{2}{3} < -2 \cdot \frac{2}{3} \][/tex]
[tex]\[ e < -\frac{4}{3} \][/tex]
So, the solution for Problem 13 is:
[tex]\[ e < -\frac{4}{3} \][/tex]
---
In summary:
- For Problem 9: [tex]\( b > 6 \)[/tex]
- For Problem 11: [tex]\( r \geq 9 \)[/tex]
- For Problem 13: [tex]\( e < -\frac{4}{3} \)[/tex]
