The solution set for the inequality -8x + 5 ≥ 9 is: (-∞, -1/2]
To solve the inequality -8x + 5 ≥ 9, we need to isolate x on one side of the inequality sign. We can do this by subtracting 5 from both sides of the inequality:
-8x + 5 - 5 ≥ 9 - 5
Simplifying the left side and the right side, we get:
-8x ≥ 4
Next, we need to isolate x by dividing both sides of the inequality by -8. Since we are dividing by a negative number, we need to reverse the inequality sign:
x ≤ -4/8
Simplifying the right side, we get:
x ≤ -1/2
Therefore, the solution set for the inequality -8x + 5 ≥ 9 is: (-∞, -1/2]
This solution set can be written in interval notation as (-∞, -1/2]. To graph the solution, we can draw a number line and shade the interval (-∞, -1/2]. The closed circle at -1/2 indicates that -1/2 is included in the solution set.