Sure, let's solve the inequality step-by-step.
We start with the inequality:
[tex]\[
\frac{x}{7} + 18 \geq 7
\][/tex]
Step 1: Isolate the term containing [tex]\( x \)[/tex]
Subtract 18 from both sides of the inequality:
[tex]\[
\frac{x}{7} + 18 - 18 \geq 7 - 18
\][/tex]
This simplifies to:
[tex]\[
\frac{x}{7} \geq -11
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex]
To eliminate the fraction, multiply both sides of the inequality by 7:
[tex]\[
7 \times \frac{x}{7} \geq 7 \times (-11)
\][/tex]
This gives:
[tex]\[
x \geq -77
\][/tex]
So, the solution to the inequality is:
[tex]\[
x \geq -77
\][/tex]
Thus, the correct option is [tex]\(\boxed{\text{B) } x \geq -77}\)[/tex].
