Solve the inequality 2/3x≤5 . Which of the following graphs shows the solution?

Answer 1

The inequality given is:
(2/3)x ≤ 5

To solve this inequality, we can multiply both sides of the inequality by (3/2), if none of the sides are negative. Since (3/2) is a positive number, we do not need to flip the inequality sign.

By multiplying both sides of the inequality by (3/2), we get:
x ≤ (5)(3/2)
x ≤ 15/2

This means that the solution to the inequality is x less than or equal to 15/2.

Reviewing the given graphs:

Graph A: Does not show x ≤ 15/2. The graph passes through (15/2, 0), indicating x = 15/2 is not part of the solution.

Graph B: Does not show x ≤ 15/2. The graph does not show x values less than or equal to 15/2.

Graph C: Shows x ≤ 15/2. The graph shows x values less than or equal to 15/2, which matches the solution to the inequality.

Graph D: Does not show x ≤ 15/2. The graph does not show x values less than or equal to 15/2.

Therefore, the graph that shows the solution to the inequality 2/3x ≤ 5 is Graph C.