Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. solve $3x > -12$ and graph the solutions. options: $x > -4$ with a number line having an open circle at -4 and arrow to the right; $x > -4$ with a number line having a closed circle at -4 and arrow to the right; $x < -4$ with a number line having a closed circle at -4 and arrow to the left; $x < -4$ with a number line having an open circle at -4 and arrow to the left.

Explanation:

Step1: Solve the inequality

Given \( 3x > -12 \), divide both sides by 3 (since 3 is positive, the inequality sign remains the same). So, \( \frac{3x}{3}>\frac{-12}{3} \), which simplifies to \( x > - 4 \).

Step2: Analyze the number line graph

For the inequality \( x > - 4 \), the solution does not include -4, so we use an open circle at -4. And the arrow should point to the right (since \( x \) is greater than -4, values to the right of -4 on the number line are the solutions). The first graph has an open circle at -4 and the arrow pointing to the right, which matches our solution \( x > - 4 \). The second graph has a closed circle (which would be for \( x\geq - 4\), but our solution is \( x > - 4\) so closed circle is incorrect). The other options have \( x < - 4\) which is the opposite of our solution, so they are incorrect.

Answer:

The first option with \( x > -4 \) and the open circle at -4 (the first graph)