Given: #3| 2x - 2| + 6= 18#
Subtract 6 from both sides:
#3| 2x - 2|= 12#
Divide both sides by 3:
#| 2x - 2|= 4#
Use the definition #|A| = {(A;A>=0),(-A;A<0):} # to break the above into two equations:
# 2x - 2= 4; 2x-2>=0# and #-(2x-2)=4; 2x-2 < 0#
Simplify the domain restrictions:
# 2x - 2= 4; 2x>=2# and #-(2x-2)=4; 2x < 2#
# 2x - 2= 4; x>=1# and #-(2x-2)=4; x < 1#
Solve the equations:
# 2x= 6; x>=1# and #2x-2=-4; x < 1#
# x= 3; x>=1# and #2x=-2; x < 1#
# x= 3; x>=1# and #x=-1; x < 1#
We can drop the domain restrictions because they are not violated:
# x= 3# and #x=-1#
Check:
#3| 2(3) - 2| + 6= 18# and #3| 2(-1) - 2| + 6= 18#
#3|4| + 6= 18# and #3| -4| + 6= 18#
#12 + 6= 18# and #12 + 6= 18#
This checks.
