To solve the inequality [tex]\(\frac{-x}{7} + 4 \geq 3x\)[/tex], follow these steps:
1. Start with the given inequality:
[tex]\[
\frac{-x}{7} + 4 \geq 3x
\][/tex]
2. Eliminate the fraction by multiplying both sides of the inequality by 7:
[tex]\[
7 \left(\frac{-x}{7} + 4\right) \geq 7 \cdot 3x
\][/tex]
3. Simplify the resulting expression:
[tex]\[
-x + 28 \geq 21x
\][/tex]
4. Collect like terms by adding [tex]\(x\)[/tex] to both sides:
[tex]\[
28 \geq 21x + x
\][/tex]
[tex]\[
28 \geq 22x
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by 22:
[tex]\[
\frac{28}{22} \geq x
\][/tex]
[tex]\[
x \leq \frac{28}{22}
\][/tex]
6. Simplify the fraction:
[tex]\[
x \leq \frac{14}{11}
\][/tex]
Thus, the inequality [tex]\(\frac{-x}{7} + 4 \geq 3x\)[/tex] simplifies to [tex]\(x \leq \frac{14}{11}\)[/tex].
So, the correct answer is:
A. [tex]\(x \leq \frac{14}{11}\)[/tex]
