Find the extraneous solution of the equation |4x−42|=−10x.

x=3 is the extraneous solution

Step-by-step explanation:

|4x-42| = -10x

Since it's absolute value and we know that there are two possibilities, we need two equations to set up to solve for x.

1st equation:

4x - 42 = -10x

2nd equation:

4x - 42 = 10x

Solve both equations for x:

1st equation:4x - 42 = -10x14x-42 = 014x=42x = 32nd equation:4x-42=10x-6x-42=0-6x=42x=-7

Plug in both values for x in the original equation to find the extraneous solution:

x=-7

|4x-42|=-10x|4(-7)-42|=-10(-7)|-28-42|=70|-70|=7070=70

x=3

|4x-42|=-10x|4(3)-42|=-10(3)|-30|=-3030≠-30

In the graph, the vertex of the parabola hits point (-1,-2). Therefore, the axis of symmetry is x = -1. It is not y = -2, since the parabola opens vertically, not horizontally.