Collecting like terms:

#50(3x-2x+7/5-3/10+9)-18=12#

#50(x+7/5-3/10+9)-18=12#

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#color(brown)("Consider inside the brackets")#

Multiply by 1 and you do not change the value. However 1 comes in many forms.

#color(green)(x+7/5-3/10+9color(white)("ddd")-> color(white)("ddd")x+[7/5 color(red)(xx1) ]-3/10+[9color(red)(xx1)]#

#color(green)( color(white)("dddddddddddddddd")->color(white)("ddd")x+[7/5color(red)(xx2/2)] -3/10+[9color(red)(xx10/10)])#

#color(green)( color(white)("dddddddddddddddd")->color(white)("ddd")x+color(white)("dd")14/10color(white)("ddd")-3/10+color(white)("dd")90/10)#

#color(green)(color(white)("dddddddddddddddd")->color(white)("ddd")x+101/10)#

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#color(brown)("Putting it all back together")#

#color(green)(50(x+101/10)-18=12)#

Add #color(red)(18)# to both sides- moves it to the right of =

#color(green)(50(x+101/10)-18color(red)(+18)=12color(red)(+18))#

#color(green)(50(x+101/10)+color(white)("dd")0color(white)("dd")=30)#

Multiply everything inside the brackets by 50

#color(green)(50x+505=30)#

Subtract 505 from both sides - moves it to the right of =

#color(green)(50x=-475)#

Divide both sides by #color(red)(50)# moves it to the right of =

#color(green)(50/color(red)(50)x=-475/color(red)(50))#

But #50/50# is the same as 1 and #1xx x# gives just #x#

#x=-(475-:5)/(50-:5)=-(95-:5)/(10-:5)=-19/2#

19 is a prime number so we can not simplify any further.

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#color(blue)("Foot note")#

First few prime numbers:

2; 3; 5; 7; 11; 13; 17; 19; 23 ........

Worth committing to memory all the primes up to and including 101