Extraneous Solution

Question

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

Answer 1

To solve absolute value problems, generate a "Case 1" in which you just drop the absolute value signs, and a "Case 2" where you replace the absolute value signs with parentheses with a negative in front like this:

Case 1

4x - 42 = -10x

14x = 42

x = 3

Case 2

-(4x - 42) = -10x

-4x + 42 = -10x

6x = -42

x = -7

To find out if one is extraneous, plug them in to the original equation to see if they work:

|4(3)-42| = -10(3)

|-30| = -30

30 = -30

This is not a true statement so x = 3 is an extraneous solution

|4(-7)-42| = -10(-7)

|-70| = 70

70 = 70

This is a true statement so x = -7 is a real solution