Question

Solve the inequality. Graph the solution.

a) y ≥ -52
b) y ≥ -56
c) y ≤ -52
d) y ≤ -56

Answer 1

The inequalities y ≥ -52, y ≥ -56, y ≤ -52, and y ≤ -56 are each graphed as horizontal lines at their respective y-values. Lines are solid to indicate 'greater than or equal to' or 'less than or equal to'. Points above (for ≥) or below (for ≤) these lines are included in the solution set.

Step-by-step explanation:

To solve the inequality and graph the solution, we need to understand what each inequality expression represents graphically. The inequalities given are:

• y ≥ -52
• y ≥ -56
• y ≤ -52
• y ≤ -56

Let's consider each one:

1. y ≥ -52: This inequality means that y is greater than or equal to -52. Graphically, this is represented by a horizontal line at y = -52 which includes all the points above it. Since y is equal to -52, we include the line itself in our solution set by drawing it as a solid line.
2. y ≥ -56: Similarly, y is greater than or equal to -56. The horizontal line is now at y = -56, with all points above this line included in the solution set, marked as a solid line to show that the line is part of the solution.
3. y ≤ -52: For this inequality, y is less than or equal to -52. The graph consists of a horizontal line at y = -52 with all points below this line (including the line itself, as a solid line).
4. y ≤ -56: In this case, y is less than or equal to -56. A horizontal line is drawn at y = -56, including all points below it in the solution set, which is indicated by the solid line again.

Each graph is a straight horizontal line since there is no x-variable present, and the inequalities only involve a y-value. The lines are solid because each inequality is 'greater than or equal to' or 'less than or equal to', not just 'greater than' or 'less than'.