# Question f01d2

Apr 1, 2017

Assuming I have interpreted your equation correctly:

$x = 157 \frac{1}{11} \leftarrow \text{ Look at the method used"->"First principles}$

#### Explanation:

Note that to trigger maths formatting you put a hash at the beginning and end of the maths part. Have a look at
https://socratic.org/help/symbols

$\textcolor{g r e e n}{\text{If your original equation is different to this then look at how}}$$\textcolor{g r e e n}{\text{I solved this one and use the same approach to solve the correct formula}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assumption - the equation is meant to be:

$\frac{51}{x} + 11 = \frac{15}{5}$

White as:

$\frac{51}{x} + \frac{11}{1} = \frac{15}{5}$

Turn everything upside down so that the $x$ is on the top of the fraction (numerator) giving:

$\frac{x}{51} + \frac{1}{11} = \frac{15}{5}$

Subtract $\textcolor{red}{\frac{1}{11}}$ from both sides so that you end up with just the $x$ term on the left of the equals.

color(green)(x/51+1/11color(red)(-1/11)" "=" "15/5color(red)(-1/11)

but $\frac{1}{11} - \frac{1}{11} = 0$

color(green)(x/51+0" "=" "15/5-1/11

Multiply both side by $\textcolor{red}{51}$ so that you end up with just $x$ on the left.

color(green)(x/51color(red)(xx51)" "=" "32/11color(red)(xx51)

color(green)(x xx(color(red)(51))/51" "=" "157 1/11 #

But $\frac{51}{51} = 1 \mathmr{and} 1 \times x = x$

$x = 157 \frac{1}{11}$