https://file.aiquickdraw.com/mathbot/file/1728472543259gb3jo7ao.jpg

The inequality is:

\[
6x + \frac{7}{3} > \frac{2}{7}x - 5
\]

### Steps to solve for \(x\):

1. **Eliminate the fractions** by multiplying the entire inequality by the least common denominator (LCD) of 3 and 7, which is 21.

\[
21 \cdot \left(6x + \frac{7}{3}\right) > 21 \cdot \left(\frac{2}{7}x - 5\right)
\]

Simplifying both sides:

\[
21 \cdot 6x + 21 \cdot \frac{7}{3} > 21 \cdot \frac{2}{7}x - 21 \cdot 5
\]

\[
126x + 49 > 6x - 105
\]

2. **Move the terms involving \(x\) to one side** and constants to the other:

\[
126x - 6x > -105 - 49
\]

\[
120x > -154
\]

3. **Solve for \(x\)** by dividing both sides by 120:

\[
x > \frac{-154}{120}
\]

Simplifying the fraction:

\[
x > \frac{-77}{60}
\]

Thus, the solution is:

\[
x > \frac{-77}{60}
\]

Would you like more details on any of the steps or additional help?

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Here are 5 related questions to deepen your understanding:

1. How do you solve inequalities involving fractions?
2. What is the least common denominator (LCD) and how is it used?
3. How do you solve linear inequalities with multiple terms involving \(x\)?
4. How does multiplying or dividing by a negative number affect the inequality sign?
5. How would you graph the solution \(x > \frac{-77}{60}\)?

**Tip**: Always simplify fractions in inequalities to make the solution clearer!

Learn how to solve the linear inequality 6x + 7/3 > 2/7x - 5 by eliminating fractions and simplifying terms. This step-by-step solution is ideal for students in Grades 9-10 who are working with algebraic inequalities.

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