Question

Find the extraneous solution of the equation |x−8|=3x.

Answer 1

Answer:

x=2

Step-by-step explanation:

1.|x-8|=3x

2. |x-8|-3x=0

3. x-8-3x=0 , -(x-8)-3x=0

4. x=-4 , x=2

5. x=all real numbers , x=2

Answer 2

Answer:

x=-4 is the extraneous solution

Step-by-step explanation:

|x−8|=3x

Lets make two equations for absolute functions. one with positive 3x and another with negative 3x

$x-8=3x$

Add 8 on both sides

$x=3x+8$

Subtract 3x from both sides

$-2x=+8$, divide both sides by -2

x=-4

$x-8=-3x$

Add 8 on both sides

$x=3x+8$

Add 3x from both sides

$4x=+8$, divide both sides by 4

x=2

Now we check with each solution

When x=-4, $|-4−8|=3(-4)$

$12=-12$, False . So x=-4 is not a solution

When x=2, $|2−8|=3(2)$

$6=6$, True . So x=2 is a solution

x=-4 is the extraneous solution