7. The number line below shows the solution set of an inequality: Which two inequalities represent the graph shown?
Answer: B
The solution set is represented by the inequalities 3x>-6 and x-4>6.
The correct inequalities that match the solution set shown in the number line are 3x>-6 and x-4>6. These inequalities effectively capture the ranges and values depicted in the graph.
A) -2x>4 and 4x
The inequality -2x>4 simplifies to x< -2, and 4x
B) 3x>-6 and x-4>6
The first inequality, 3x>-6, simplifies to x>-2. The second inequality, x-4>6, simplifies to x>10. Together, they represent a solution set that is consistent with the graph, which shows values greater than -2 and greater than 10, confirming this option as correct.
C) 4x
The inequality 4x
D) 4x
This option is identical to Option C, thus carrying the same implications. The values represented by this set are incompatible with the number line shown, which does not include the ranges specified here.
Conclusion
Option B is definitively correct as it accurately represents the solution set illustrated in the number line, demonstrating the ranges of x that are valid. All other options fail to align with the graph, either by including incorrect values or ranges that do not correspond to the depicted solution set.