What is the graph of the solutions to the inequality -(1/2)x - 6 > 4 - 3x?

To determine the correct answer, it's important to solve the inequality and understand the nature of the solutions.

Starting with the given inequality:

-(1/2)x - 6 > 4 - 3x

To eliminate the fractions and simplify the inequality, you can multiply the entire inequality by -2, making sure to reverse the inequality sign:

x + 12 < -8 + 6x

Now, rearranging the terms gives:

-5x < -8 - 12

Adding 12 to both sides results in:

-5x < -20

Dividing each side by -5 (again reversing the inequality sign) leads to:

x > 4

Now, interpreting the inequality x > 4 shows that the solution includes all numbers greater than 4. Graphing this means shading to the right of the number line starting at 4, not including 4 itself, as the inequality does not include equality (indicated by a "greater than" sign).

Thus, the graph of the solutions to the inequality is one where all numbers greater than 4 are included, which corresponds to the first choice.