To solve for [tex]\( x \)[/tex] in the inequality [tex]\(\frac{x}{11} - 6 \geq -20\)[/tex], follow these steps:
1. Isolate the term with the variable [tex]\( x \)[/tex]:
Start by getting rid of the constant term on the left side.
[tex]\[
\frac{x}{11} - 6 \geq -20
\][/tex]
Add 6 to both sides to move the -6 from the left side:
[tex]\[
\frac{x}{11} - 6 + 6 \geq -20 + 6
\][/tex]
Simplify both sides:
[tex]\[
\frac{x}{11} \geq -14
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
Now, multiply both sides of the inequality by 11 to isolate [tex]\( x \)[/tex]. Since 11 is a positive number, the direction of the inequality remains the same.
[tex]\[
\frac{x}{11} \times 11 \geq -14 \times 11
\][/tex]
Simplify:
[tex]\[
x \geq -154
\][/tex]
Thus, the solution to the inequality [tex]\(\frac{x}{11} - 6 \geq -20\)[/tex] is:
[tex]\( x \geq -154 \)[/tex]
The correct answer is B) [tex]\( x \geq -154 \)[/tex].
