Final answer:
The inequality -5x - 15 > 10*20x simplifies to x < -3 / 41. None of the provided options (2, -1, 0, 1) represent this solution set since they are single values and not number lines.
Step-by-step explanation:
The question asks us to solve the inequality –5x – 15 > 10 20x and determine which number line represents the solution set. To solve the inequality, we need to simplify and solve for x.
Step 1: Simplify the inequality by combining like terms.
-5x – 15 > 200x
Step 2: Add 5x to both sides to get all the x terms on one side.
– 15 > 205x
Step 3: Divide both sides by 205 to isolate x.
– 15 / 205 > x
x < – 15 / 205
Step 4: Simplify the fraction.
x < – 3 / 41
The answer would be a number line with a shaded region to the left of – 3 / 41, which indicates that the solution includes all numbers less than – 3 / 41. However, the options provided (A. 2, B. -1, C. 0, D. 1) do not contain a number line but rather single values, therefore none of the options correctly represents the solution set to the inequality.