Question #cfc36

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Question #cfc36

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Answer 1 · 2017-10-17T16:37:15

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

Explanation:

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

You can solve it by using proportion:

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

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

Answer 2 · 2017-10-17T16:52:29

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

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

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

$First principles method$ $color(red)("First principles method")$

If we can change the $\frac{1}{4}$ $1/4$ bit from $\frac{x}{4}$ $x/4$ into 1 then $x \times 1 \to x$ $x xx1->x$ and we have solved it.

Write as

$x \times \frac{1}{4} = \frac{3}{11}$ $color(green)(x xx1/4=3/11)$

Multiply both sides by $4$ $color(red)(4)$

$x \times \frac{1}{4} \times 4 ddd = ddd \frac{3}{11} \times 4$ $color(green)(x xx1/4color(red)(xx4)color(white)("ddd")=color(white)("ddd")3/11color(red)(xx4))$

$dd x \times \frac{4}{4} dddd = ddd \frac{3 \times 4}{11}$ $color(green)(color(white)("dd")x xx(color(red)(4))/4color(white)("dddd")=color(white)("ddd")(3color(red)(xx4))/11)$

$dd x \times 1 ddddd = ddd \frac{12}{11}$ $color(white)("dd")x xx1color(white)("ddddd") =color(white)("ddd")12/11$

$x = \frac{12}{11}$ $x=12/11$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Shortcut method$ $color(red)("Shortcut method ")$

$Basically this is just remembering what happens with first principles$ $color(brown)("Basically this is just remembering what happens with first principles")$

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

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

So $\frac{x}{4} = \frac{3}{11} d \to d d x = \frac{3}{11} \times 4$ $x/4=3/11 color(white)("d")->color(white)("d")color(white)("d")x=3/11xx4$

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

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Question #cfc36

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