# Question #cfc36

Oct 17, 2017

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

#### Explanation:

$\setminus \frac{x}{4} = \setminus \frac{3}{11}$

You can solve it by using proportion:

$x = \setminus \frac{4 \times 3}{11} = \setminus \frac{12}{11}$

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

Oct 17, 2017

$x = \frac{12}{11}$

#### Explanation:

Have a look at https://socratic.org/help/symbols for formatting. Note the hash at the beginning and end of the typed text. This triggers the implementation of mathematical formatting.

Given: $\frac{x}{4} = \frac{3}{11}$

Our target is to have $x$ on its own on one side of the equals and all the numbers on the other side

$\textcolor{red}{\text{First principles method}}$

If we can change the $\frac{1}{4}$bit from $\frac{x}{4}$ into 1 then $x \times 1 \to x$ and we have solved it.

Write as

$\textcolor{g r e e n}{x \times \frac{1}{4} = \frac{3}{11}}$

Multiply both sides by $\textcolor{red}{4}$

$\textcolor{g r e e n}{x \times \frac{1}{4} \textcolor{red}{\times 4} \textcolor{w h i t e}{\text{ddd")=color(white)("ddd}} \frac{3}{11} \textcolor{red}{\times 4}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dd")x xx(color(red)(4))/4color(white)("dddd")=color(white)("ddd}} \frac{3 \textcolor{red}{\times 4}}{11}}$

$\textcolor{w h i t e}{\text{dd")x xx1color(white)("ddddd") =color(white)("ddd}} \frac{12}{11}$

$x = \frac{12}{11}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{red}{\text{Shortcut method }}$

$\textcolor{b r o w n}{\text{Basically this is just remembering what happens with first principles}}$

Consider the 4 from $\frac{x}{4}$

This is $x \div 4$ so move the 4 to the other side of the equals and use the opposite action to divide. Which is multiply.

So $\frac{x}{4} = \frac{3}{11} \textcolor{w h i t e}{\text{d")->color(white)("d")color(white)("d}} x = \frac{3}{11} \times 4$

$x = \frac{12}{11}$