Question #e198c

2 Answers
Jan 17, 2018

just solve...

Explanation:

so
150x + 70 - 100x - 15 + 450 - 18 = 12

=> 50x + 55 + 450 = 30

=> 50x = -420 -55

=> x= -475/50 = -19/2

hope u find it helpful :)

Jan 19, 2018

Assumption: The question is 50(3x+7/5-2x-3/10+9)-18=12

x=-19/2

A lot of detail given so you can see where everything comes from. Get used to these and you will start to jump steps and be much faster.

Explanation:

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