Question #e198c

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Question #e198c

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Answer 1 · 2018-01-17T15:49:06

just solve...

Explanation:

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

$\Rightarrow 50 x + 55 + 450 = 30$ $=> 50x + 55 + 450 = 30$

$\Rightarrow 50 x = - 420 - 55$ $=> 50x = -420 -55$

$\Rightarrow x = - \frac{475}{50} = - \frac{19}{2}$ $=> x= -475/50 = -19/2$

hope u find it helpful :)

Answer 2 · 2018-01-19T10:36:51

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

$x = - \frac{19}{2}$ $x=-19/2$

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:

$50 (3 x - 2 x + \frac{7}{5} - \frac{3}{10} + 9) - 18 = 12$ $50(3x-2x+7/5-3/10+9)-18=12$

$50 (x + \frac{7}{5} - \frac{3}{10} + 9) - 18 = 12$ $50(x+7/5-3/10+9)-18=12$
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$Consider inside the brackets$ $color(brown)("Consider inside the brackets")$

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

$x + \frac{7}{5} - \frac{3}{10} + 9 ddd \to ddd x + [\frac{7}{5} \times 1] - \frac{3}{10} + [9 \times 1]$ $color(green)(x+7/5-3/10+9color(white)("ddd")-> color(white)("ddd")x+[7/5 color(red)(xx1) ]-3/10+[9color(red)(xx1)]$

$dddddddddddddddd \to ddd x + [\frac{7}{5} \times \frac{2}{2}] - \frac{3}{10} + [9 \times \frac{10}{10}]$ $color(green)( color(white)("dddddddddddddddd")->color(white)("ddd")x+[7/5color(red)(xx2/2)] -3/10+[9color(red)(xx10/10)])$

$dddddddddddddddd \to ddd x + dd \frac{14}{10} ddd - \frac{3}{10} + dd \frac{90}{10}$ $color(green)( color(white)("dddddddddddddddd")->color(white)("ddd")x+color(white)("dd")14/10color(white)("ddd")-3/10+color(white)("dd")90/10)$

$dddddddddddddddd \to ddd x + \frac{101}{10}$ $color(green)(color(white)("dddddddddddddddd")->color(white)("ddd")x+101/10)$
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$Putting it all back together$ $color(brown)("Putting it all back together")$

$50 (x + \frac{101}{10}) - 18 = 12$ $color(green)(50(x+101/10)-18=12)$

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

$50 (x + \frac{101}{10}) - 18 + 18 = 12 + 18$ $color(green)(50(x+101/10)-18color(red)(+18)=12color(red)(+18))$

$50 (x + \frac{101}{10}) + dd 0 dd = 30$ $color(green)(50(x+101/10)+color(white)("dd")0color(white)("dd")=30)$

Multiply everything inside the brackets by 50

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

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

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

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

$\frac{50}{50} x = - \frac{475}{50}$ $color(green)(50/color(red)(50)x=-475/color(red)(50))$

But $\frac{50}{50}$ $50/50$ is the same as 1 and $1 \times x$ $1xx x$ gives just $x$ $x$

$x = - \frac{475 \div 5}{50 \div 5} = - \frac{95 \div 5}{10 \div 5} = - \frac{19}{2}$ $x=-(475-:5)/(50-:5)=-(95-:5)/(10-:5)=-19/2$

19 is a prime number so we can not simplify any further.
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$Foot note$ $color(blue)("Foot note")$

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

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Question #e198c

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