To solve the given inequality [tex]\( 15 < 4 + x \)[/tex], we need to isolate the variable [tex]\( x \)[/tex]. Here is a step-by-step solution:
1. Start with the inequality:
[tex]\[
15 < 4 + x
\][/tex]
2. To isolate [tex]\( x \)[/tex], subtract 4 from both sides of the inequality. This helps to move the constant term on the right side to the left side. So, we perform:
[tex]\[
15 - 4 < 4 + x - 4
\][/tex]
3. Simplify both sides of the inequality:
[tex]\[
11 < x
\][/tex]
This tells us that [tex]\( x \)[/tex] must be greater than 11. Thus, the correct answer is:
D. [tex]\( x > 11 \)[/tex]
