Solve the inequality. Give the solution set in both interval and graph forms.
StartFraction 3 x minus 4 Over negative 2 EndFraction greater than 4

To solve the inequality 

\[
\frac{3x - 4}{-2} > 4,
\]

we'll start by isolating the variable \( x \). Here are the steps:

### Step 1: Multiply both sides by \(-2\)
Since we are multiplying by a negative number, the direction of the inequality will change:

\[
3x - 4 < 4 \times (-2)
\]

Simplifying the right side:

\[
3x - 4 < -8
\]

### Step 2: Add 4 to both sides
To isolate \( 3x \), add 4 to both sides:

\[
3x < -8 + 4
\]

Simplifying the right side:

\[
3x < -4
\]

### Step 3: Divide by 3
Finally, divide both sides by 3 to solve for \( x \):

\[
x < \frac{-4}{3}
\]

### Solution Set in Interval Form:
The solution set in interval form is:

\[
(-\infty, -\frac{4}{3})
\]

### Graph of the Solution:
To graph the solution, draw a number line, place an open circle at \( x = -\frac{4}{3} \), and shade everything to the left of this point to indicate all numbers less than \( -\frac{4}{3} \).

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Would you like any details or have any questions?

Here are 5 related questions for further exploration:

1. How does the inequality change if the fraction were positive?
2. What happens to the inequality when the right side is a variable expression instead of a constant?
3. How would you solve \( \frac{3x - 4}{2} > 4 \)?
4. What is the solution if the inequality were \( \leq \) instead of \( > \)?
5. Can you describe the graphical difference between a strict inequality (>) and a non-strict one (≥)?

**Tip:** Always remember that multiplying or dividing an inequality by a negative number reverses the inequality sign!

Learn how to solve the inequality (3x - 4) / -2 > 4 with a detailed step-by-step solution. This problem covers key concepts in algebra, including solving inequalities with fractional expressions and understanding the direction of inequality signs when multiplying by negative numbers. Suitable for students in Grades 9-12.

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