How do you solve #3( x - 1) + \frac { 3} { 5} = 3#?

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Answer 1 · 2017-04-19T21:18:48

#x=9/5#

#color(blue)("Preamble")#

The technique for moving values to the other side of the equals sign:

For add or subtract change it into 0
For multiply or divide turn it into 1

The shortcuts is just remembering the consequences of the above and applying it.
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#color(blue)("Answering the question using first principles")#

Given: #" "3(x-1)+3/5=3#

#color(magenta)("First we isolate the group that has "x" in it"->#subtract #color(red)(3/5)# from both sides

#color(green)(3(x-1)+3/5color(red)(-3/5)" "=" "3color(red)(-3/5) )#

#3(x-1)+0" "=" "12/5#

Divide both sides by #color(red)(3)#

#color(green)(3/(color(red)(3))(x-1)" "=" "12/(5color(red)(xx3))#

#x-1" "=" "4/5#
............................................................................................
#color(magenta)("Now we isolate "x)#

Add #color(red)(1)# to both sides

#color(green)(x-1color(red)(+1)" "=" "4/5color(red)(+1)#

#x+0" "=" "9/5#

#x=9/5#