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To solve the inequality \(\frac{4x - 5}{7} > 2x + 1\), we can follow these steps:

### Step 1: Eliminate the denominator.
Multiply both sides of the inequality by 7 to get rid of the denominator.

\[
4x - 5 > 7(2x + 1)
\]

Simplifying the right-hand side:

\[
4x - 5 > 14x + 7
\]

### Step 2: Isolate the variable.
Now, we want to bring all terms involving \(x\) on one side and the constants on the other side. First, subtract \(4x\) from both sides:

\[
-5 > 10x + 7
\]

Next, subtract 7 from both sides:

\[
-12 > 10x
\]

### Step 3: Solve for \(x\).
Now, divide both sides by 10:

\[
\frac{-12}{10} > x
\]

Simplifying the fraction:

\[
-1.2 > x
\]

This can be rewritten as:

\[
x < -1.2
\]

### Final Answer:
The solution to the inequality is \(x < -1.2\).

Let me know if you'd like further explanation, and here are some related questions to explore:

1. What happens if the inequality sign is reversed?
2. How would you solve this inequality if it had \(\geq\) instead of \(>\)?
3. Can you represent the solution on a number line?
4. What are the steps to solve a similar inequality with a negative coefficient of \(x\)?
5. How does solving an equation differ from solving an inequality?

**Tip:** When multiplying or dividing by a negative number in inequalities, remember to reverse the inequality sign!

Solve the inequality (4x - 5)/7 > 2x + 1.

Learn how to solve the inequality (4x - 5)/7 > 2x + 1 with detailed algebraic steps. This problem covers core algebraic concepts like solving inequalities, linear equations, and isolating variables. Suitable for Grades 8-10 students.

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