Question

The Boss Battle, Sole This Math Problem :)

Answer 1

Answer:

x = -7, x = 1

Extraneous Solution: x = -7

Step-by-step explanation:

If |x - 5| is positive

 

        $|x - 5| = 2(x + 1)\\\\x - 5 = 2x +2\\\\x - 7 = 2x\\\\-7 = x$

If |x - 5| is negative

         $|x - 5| = 2(x + 1)\\\\-x + 5 = 2x + 2\\\\5 = 3x + 2\\\\3 = 3x\\\\x = 1$

Now, check for extraneous:

$|-7 - 5| = 2(-7 + 1)\\\\|-12| = 2(-6)\\\\|-12|=-12$

$|1-5|=2(1+1)\\\\|-4| = 2(2)\\\\4 = 4$

-7 is extraneous because the absolute value of |-12| ≠ -12

-Chetan K