To solve the inequality [tex]\( \frac{x}{9} + 3 < 4 \)[/tex], let's go through the steps methodically:
1. Start with the given inequality:
[tex]\[
\frac{x}{9} + 3 < 4
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex]:
- Subtract 3 from both sides of the inequality to get rid of the constant term on the left side.
[tex]\[
\frac{x}{9} + 3 - 3 < 4 - 3
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{x}{9} < 1
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], multiply both sides of the inequality by 9.
[tex]\[
\left(\frac{x}{9}\right) \cdot 9 < 1 \cdot 9
\][/tex]
Simplifying this, we get:
[tex]\[
x < 9
\][/tex]
Therefore, the solution to the inequality [tex]\( \frac{x}{9} + 3 < 4 \)[/tex] is [tex]\( x < 9 \)[/tex]. Thus, the correct answer is:
A. [tex]\( x < 9 \)[/tex]
