Question

Question #e198c

Answer 1

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 :)

Answer 2

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