Question

| x - 1 | = 5x + 10
Check for extraneous solutions.

Answer 1

[x-1]=5x+10

We have two equations:
1) x-1=5x+10

x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4

2) x-1=-(5x+10)

x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2

we have two  possible solutions:
solution₁;       x=-11/4
solution₂:       x=-3/2

we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4  - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4  + 10
[-15/4]=(-55+40) /4
15/4≠-15/4   This solution don´t work.

2) x=-3/2
[x-1]=5x+10
[-3/2  - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2  + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.

Therefore:

Answer: x=-3/2.

Answer 2

Solution #1 $x-1=5x+10$

$x-1=5x+10$

$x-5x=10+1$

$-4x=11$

$x=-11/4$

Solution #2 $x-1=-(5x+10)$

$x-1=-(5x+10)$

$x-1=-5x-10$

$x+5x=-10+1$

$6x=-9$

$x=-9/6=-3/2$  

We have two  possible outcomes.