The problem asks to solve the inequality $\frac{x+2}{4} > \frac{x}{3} + 2$ and then to graph the solution set.

1. Problem Description

The problem asks to solve the inequality $\frac{x+2}{4} > \frac{x}{3} + 2$ and then to graph the solution set.

2. Solution Steps

First, we multiply both sides of the inequality by 12 (the least common multiple of 3 and 4) to eliminate the fractions:

$12 \cdot \frac{x+2}{4} > 12 \cdot (\frac{x}{3} + 2)$

$3(x+2) > 4x + 24$

Now we distribute on the left side:

$3x + 6 > 4x + 24$

Next, we subtract $3x$ from both sides:

$6 > x + 24$

Now, we subtract 24 from both sides:

$6 - 24 > x$

$-18 > x$

This is equivalent to $x < -18$.

To graph the solution set, we draw a number line. We place an open circle at -18 to indicate that -18 is not included in the solution set. Then, we shade the number line to the left of -18 to indicate all values less than -

1

8.

3. Final Answer

The solution is $x < -18$.