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

Study for the Praxis Elementary Education Mathmatics test (5003). Engage with flashcards and multiple-choice questions. Each question provides hints and detailed explanations to prepare you to excel on exam day!

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.