To solve the inequality [tex]\(\frac{b}{3} < 12\)[/tex], follow these steps:
1. Isolate the variable [tex]\( b \)[/tex]:
To isolate [tex]\( b \)[/tex], we need to eliminate the fraction. The fraction [tex]\(\frac{b}{3}\)[/tex] means [tex]\( b \)[/tex] is divided by 3. To undo this division, we should multiply both sides of the inequality by 3.
[tex]\[
\frac{b}{3} < 12
\][/tex]
Multiply both sides by 3:
[tex]\[
3 \cdot \frac{b}{3} < 12 \cdot 3
\][/tex]
2. Simplify the inequality:
On the left side, [tex]\( 3 \)[/tex] and [tex]\( \frac{1}{3} \)[/tex] cancel each other out, leaving just [tex]\( b \)[/tex]. On the right side, multiply 12 by 3:
[tex]\[
b < 36
\][/tex]
So, the solution to the inequality [tex]\(\frac{b}{3} < 12\)[/tex] is:
[tex]\[
b < 36
\][/tex]
This means that [tex]\( b \)[/tex] must be any number less than 36 to satisfy the given inequality.
