Final answer:
To solve and graph the inequality −12x + 5 ≥ −19, solve for x to get x ≤ 2. On the number line, represent this with a closed circle at x = 2 and shade to the left to show all values less than or equal to 2 are included.
Step-by-step explanation:
To graph the solution to the inequality −12x + 5 ≥ −19, we first need to solve the inequality for x. We do this by isolating the variable on one side of the inequality. Here are the steps:
Add 12x to both sides: 5 ≥ 12x − 1To represent this on the number line, we draw a number line and shade the area that includes all numbers less than or equal to 2. Since the inequality is ≥, we use a closed circle at x = 2 to indicate that the value 2 is included in the solution set.
When graphing a horizontal line such as f(x) = 20 for 0 ≤ x ≤ 20, we would simply draw the line at y = 20 and ensure it only spans from x = 0 to x = 20 on the graph. This line's slope is zero, indicating no change in the y-value as x increases. In the given inequality, we are not dealing with a function's graph but a graphical representation on a number line.