Let's solve the inequality:

\[
4x - 6 > 6x - 20
\]

### Step 1: Move all terms involving \(x\) to one side.

Subtract \(6x\) from both sides:

\[
4x - 6 - 6x > -20
\]

This simplifies to:

\[
-2x - 6 > -20
\]

### Step 2: Move the constant terms to the other side.

Add 6 to both sides:

\[
-2x > -14
\]

### Step 3: Solve for \(x\).

Divide both sides by \(-2\). Remember that dividing by a negative number reverses the inequality:

\[
x < 7
\]

### Final solution:
\[
x < 7
\]

Would you like more details or have any questions about this solution?

Here are five related questions to practice:
1. Solve: \(3x - 5 > 2x + 1\).
2. Solve: \(2x + 7 < 5x - 9\).
3. Solve: \(8 - 2x \geq 4x + 10\).
4. Solve: \(5x - 3 < 7x + 11\).
5. Solve: \(9x + 4 > 3x - 8\).

**Tip**: Always remember to reverse the inequality sign when you multiply or divide by a negative number.

This page provides a step-by-step guide to solving the inequality 4x - 6 > 6x - 20. Learn how to move terms involving x, simplify the equation, and apply the properties of inequalities, including reversing the inequality when dividing by a negative. Suitable for students in Grades 7-9.

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