Question

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

Answer 1

x=2

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

x=-4 is the extraneous solution

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