Question

Which of the following graphs in the xy-plane could be used to solve graphically the inequality x-2<-2(x+1)x-2<-2(x+1) and shows the solution to the inequality?

1) Graph A: y = x - 2
2) Graph B: y = -2(x + 1)
3) Graph C: y = -2x - 2
4) Graph D: y = 2x + 2

Answer 1

To graphically solve the inequality x - 2 < -2(x + 1), graph both y = x - 2 (Graph A) and y = -2x - 2 (Graph C), and then shade the area where Graph A is below Graph C.

Step-by-step explanation:

The student asked which of the following graphs in the xy-plane could be used to solve graphically the inequality x - 2 < -2(x + 1) and shows the solution to the inequality. To solve this graphically, you need to compare two linear equations: Graph A: y = x - 2, and Graph B: y = -2(x + 1).

However, since we are solving for an inequality rather than an equation, we must shade the area that represents the solution set. In this context, we want the region where the graph of y = x - 2 is below the graph of y = -2(x + 1).

Simplified, Graph B is y = -2x - 2. Looking at the options given, Graph A corresponds to y = x - 2 and Graph C corresponds to y = -2x - 2. Therefore, to represent the inequality x - 2 < -2(x + 1), we should graph both equations and shade the area where the graph of Graph A is below the graph of Graph C. Hence, you should combine Graph A and Graph C to solve the inequality graphically.