Question 14

The graph representing the solution of x + 5 ≤ 3 is A.

The inequality x + 5 ≤ 3 can be simplified to x ≤ -2. The graph that illustrates all values of x that are less than or equal to -2 will represent the solution correctly.

A) M-75A.png

This graph accurately depicts the solution x ≤ -2, with a solid line extending to the left from -2, indicating that all values less than or equal to -2 are included in the solution set.

B) M-75B.png

This graph incorrectly shows a solution that does not include -2 and extends to the right, which does not satisfy the inequality x + 5 ≤ 3. Thus, it misrepresents the solution.

C) M-75C.png

This graph also fails to depict the correct solution as it represents values greater than -2. The inequality x + 5 ≤ 3 requires values less than or equal to -2, making this option incorrect.

D) M-75D.png

This graph is incorrect as it does not include -2 and extends to the right. It does not represent the solution to the inequality x + 5 ≤ 3, which requires values less than or equal to -2.

Conclusion

Graph A is the only option that correctly represents the solution to the inequality x + 5 ≤ 3, as it includes all values less than or equal to -2. The other options fail to satisfy the condition of the inequality, thus confirming A as the definitive correct choice.