Question

Which of the following options correctly represents the solution to the inequality y - 6 < -2| x |?

A) y < -2| x | + 6
B) y > -2| x | + 6
C) y < 2| x | - 6
D) y > 2| x | - 6

Answer 1

The solution to the inequality y - 6 < -2| x | is y < -2| x | + 6, represented by option A. It describes the region below the line -2| x | + 6 in the coordinate plane. The correct option is A.

Step-by-step explanation:

To solve the inequality y - 6 < -2| x |, we want to isolate y. By adding 6 to both sides of the inequality, we obtain:

y < -2| x | + 6

This simplifies the original inequality, providing us with the correct representation of the solution, which corresponds to option A: y < -2| x | + 6.

This inequality describes the region below the graph of the line -2| x | + 6 in the coordinate plane, and since absolute value is involved, the graph will consist of two rays sloping downwards away from the y-axis. The correct option is A.