To solve the inequality \(4 - 2y < 6x\), we can rearrange it to express \(y\) in terms of \(x\). Here's how you can approach it:

### Step 1: Isolate the \(y\) term
Given:
\[
4 - 2y < 6x
\]

Subtract 4 from both sides:
\[
-2y < 6x - 4
\]

### Step 2: Solve for \(y\)
Divide both sides by \(-2\). Remember, when dividing or multiplying both sides of an inequality by a negative number, you must reverse the inequality sign:
\[
y > \frac{6x - 4}{-2}
\]

Simplify the right-hand side:
\[
y > -3x + 2
\]

### Interpretation:
The solution to the inequality is \(y > -3x + 2\). This describes a region above the line \(y = -3x + 2\) on the coordinate plane.

### Step 3: Graphical Representation
If you were to graph this inequality:
- The line \(y = -3x + 2\) would be drawn as a dashed line (because the inequality is strict: \(>\), not \(\geq\)).
- The region above this line would be shaded, indicating where the inequality holds true.

Would you like more details or have any questions?

### Related Questions:
1. What is the slope of the line \(y = -3x + 2\)?
2. How would the graph of the inequality \(y > -3x + 2\) differ if it were \(y \geq -3x + 2\)?
3. For \(x = 1\), what is the range of possible values for \(y\) according to the inequality \(y > -3x + 2\)?
4. How would the inequality change if we added 5 to both sides of the original equation \(4 - 2y < 6x\)?
5. What does the inequality \(y > -3x + 2\) tell you about the relationship between \(x\) and \(y\)?

### Tip:
When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number. This is crucial to getting the correct solution.

Learn how to solve the inequality 4 - 2y < 6x with a detailed step-by-step solution. This problem covers key concepts in inequalities and linear equations. Suitable for students in Grades 9-12.

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