Solve:
#2(4z-1)=3(z+2)#
Expand.
#8z-2=3z+6#
Subtract #3z# from both sides.
#8z-3z-2=color(red)cancel(color(black)(3z))+6-color(red)cancel(color(black)(3z))#
Simplify.
#5z-2=6#
Add #2# to both sides.
#5z-color(red)cancel(color(black)(2))+color(red)cancel(color(black)(2))=6+2#
Simplify.
#5z=8#
Divide both sides by #5#.
#(color(red)cancel(color(black)(5))^1z)/color(red)cancel(color(black)(5))^1=8/5#
#z=8/5#
We can convert the improper fraction #8/5# to a mixed number, #color(red)(a) color(blue)(b)/color(green)(c)#. Divide the numerator by the denominator by long division to get a whole-number quotient and a remainder.
#8-:color(green)(5)= color(red)(1), "remainder" color(blue)(3)#
The whole number #color(red)1# is the whole number of the mixed number, the remainder #color(blue)3# is the numerator, and the divisor is the denominator #color(green)5#.
#8/5=color(red)(1) color(blue)(3)/color(green)(5#
The decimal number is #8-:5=1.6#