Solve the inequality for [tex]\( x \)[/tex]:

[tex]\[ \frac{x}{5} + 7 \ \textgreater \ 5 \][/tex]

Select one:
A. [tex]\( x \ \textgreater \ 65 \)[/tex]
B. [tex]\( x \ \textless \ -10 \)[/tex]
C. [tex]\( x \ \textgreater \ -2 \)[/tex]
D. [tex]\( x \ \textgreater \ -10 \)[/tex]



Answer :

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]