How to find the solution of |a-4|=3a-6

For

|a|=b, solve for

a=b and a=-b

so

|a-4|=3a-6

solve

a-4=3a-6 and a-4 = - (3a-6)

first one

a-4=3a-6

minus a from both sides

-4=2a-6

add 6 to both sides

2=2a

divide by 2

1=a

other

a-4 = - (3a-6)

a-4=-3a+6

add 3a both sides

4a-4=6

add 4 to both sides

4a=10

divide by 4

a=10/4

a=5/2

a=5/2 and 1