Which graph represents the solution of x + 5 ≤ 3?

Rationale

Graph A represents the solution of x + 5 ≤ 3.

This inequality simplifies to x ≤ -2, indicating that the solution set includes all values of x that are less than or equal to -2. The graph must therefore show a solid dot at -2 and a shaded line extending to the left, representing all numbers less than -2.

A (M-75A.png) CORRECT

This graph accurately depicts the inequality x + 5 ≤ 3 by showing a solid dot at -2 and a shaded region extending leftward, indicating that all values less than or equal to -2 are included in the solution set.

B (M-75B.png) YOUR ANSWER

This graph shows a solid dot at -2, but the shading extends to the right. This incorrectly represents the solution, as the inequality states that x must be less than or equal to -2, not greater than.

C (M-75C.png) YOUR ANSWER

This graph features a dashed line at -2, which is incorrect as it implies that -2 is not included in the solution. The inequality specifically allows for -2 to be part of the solution, requiring a solid dot instead.

D (M-75D.png) YOUR ANSWER

This graph incorrectly displays a solid dot at -2 with no shading. This fails to represent the inequality x + 5 ≤ 3, as the solution must encompass all values less than or equal to -2, which requires shading to the left.

Conclusion

The solution to the inequality x + 5 ≤ 3 is represented by all values less than or equal to -2, which is correctly shown in Graph A. The other graphs misrepresent the necessary shading or the inclusion of -2, illustrating the importance of accurately interpreting and graphing inequalities on a number line.

Which graph represents the solution of x + 5 ≤ 3?

Graph A represents the solution of x + 5 ≤ 3.

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