To solve the inequality [tex]\(\frac{x}{5} + 7 > 5\)[/tex], we will isolate [tex]\(x\)[/tex] step-by-step as follows:
1. Subtract 7 from both sides of the inequality to get rid of the constant term on the left side:
[tex]\[
\frac{x}{5} + 7 - 7 > 5 - 7
\][/tex]
This simplifies to:
[tex]\[
\frac{x}{5} > -2
\][/tex]
2. Multiply both sides of the inequality by 5 to eliminate the fraction. Multiplying both sides by 5 will not change the direction of the inequality because 5 is a positive number:
[tex]\[
5 \cdot \frac{x}{5} > 5 \cdot (-2)
\][/tex]
This simplifies to:
[tex]\[
x > -10
\][/tex]
Thus, the solution to the inequality [tex]\(\frac{x}{5} + 7 > 5\)[/tex] is [tex]\(x > -10\)[/tex].
Therefore, the correct choice is:
d. [tex]\(x > -10\)[/tex]
