To solve the inequality [tex]\( 3b - 7 < 32 \)[/tex], follow these steps:
1. Start with the given inequality:
[tex]\[
3b - 7 < 32
\][/tex]
2. Add 7 to both sides of the inequality to isolate the term involving [tex]\( b \)[/tex]:
[tex]\[
3b - 7 + 7 < 32 + 7
\][/tex]
This simplifies to:
[tex]\[
3b < 39
\][/tex]
3. Next, divide both sides of the inequality by 3 to solve for [tex]\( b \)[/tex]:
[tex]\[
\frac{3b}{3} < \frac{39}{3}
\][/tex]
This simplifies to:
[tex]\[
b < 13
\][/tex]
Therefore, the solution to the inequality [tex]\( 3b - 7 < 32 \)[/tex] is [tex]\( b < 13 \)[/tex].
From the given options:
A. [tex]\( b < 5 \)[/tex]
B. [tex]\( b < 39 \)[/tex]
C. [tex]\( b < 13 \)[/tex]
D. [tex]\( b < 8.33 \)[/tex]
The correct option is:
C. [tex]\( b < 13 \)[/tex]
