# Question e198c

Jan 17, 2018

just solve...

#### Explanation:

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

$\implies 50 x + 55 + 450 = 30$

$\implies 50 x = - 420 - 55$

$\implies x = - \frac{475}{50} = - \frac{19}{2}$

hope u find it helpful :)

Jan 19, 2018

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

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

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:

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

$50 \left(x + \frac{7}{5} - \frac{3}{10} + 9\right) - 18 = 12$
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$\textcolor{b r o w n}{\text{Consider inside the brackets}}$

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)]#

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddd}} x + \left[\frac{7}{5} \textcolor{red}{\times \frac{2}{2}}\right] - \frac{3}{10} + \left[9 \textcolor{red}{\times \frac{10}{10}}\right]}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddd")x+color(white)("dd")14/10color(white)("ddd")-3/10+color(white)("dd}} \frac{90}{10}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddd}} x + \frac{101}{10}}$
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$\textcolor{b r o w n}{\text{Putting it all back together}}$

$\textcolor{g r e e n}{50 \left(x + \frac{101}{10}\right) - 18 = 12}$

Add $\textcolor{red}{18}$ to both sides- moves it to the right of =

$\textcolor{g r e e n}{50 \left(x + \frac{101}{10}\right) - 18 \textcolor{red}{+ 18} = 12 \textcolor{red}{+ 18}}$

$\textcolor{g r e e n}{50 \left(x + \frac{101}{10}\right) + \textcolor{w h i t e}{\text{dd")0color(white)("dd}} = 30}$

Multiply everything inside the brackets by 50

$\textcolor{g r e e n}{50 x + 505 = 30}$

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

$\textcolor{g r e e n}{50 x = - 475}$

Divide both sides by $\textcolor{red}{50}$ moves it to the right of =

$\textcolor{g r e e n}{\frac{50}{\textcolor{red}{50}} x = - \frac{475}{\textcolor{red}{50}}}$

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

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

19 is a prime number so we can not simplify any further.
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$\textcolor{b l u e}{\text{Foot note}}$

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