# Question a3e2c

Oct 28, 2017

$x = \frac{17}{36}$

#### Explanation:

We can set up an equation to solve the value of the number, $x$.

The number $= x$

Multiplying the number by $3 = 3 x$

Subtracting $\frac{2}{3}$ from that $= 3 x - \frac{2}{3}$

The result is $\frac{3}{4}$, so

$3 x - \frac{2}{3} = \frac{3}{4}$

We can then solve our equation:

$3 x - \frac{2}{3} = \frac{3}{4}$

Add $\frac{2}{3}$ to both sides:

$3 x = \frac{3}{4} + \frac{2}{3}$

$3 x = \frac{17}{12}$

Divide both sides by $3$ to get the value of $x$:

$x = \frac{17}{36}$

You can then check your answer (optional):

$\frac{17}{36} \cdot 3 = \frac{17}{12}$

$\frac{17}{12} - \frac{2}{3} = \frac{3}{4}$

Oct 28, 2017

$\frac{17}{36}$

#### Explanation:

Breaking the question down into its component parts.

A number ......................................................... $x$
is multiplied by 3 ...........................................$3 x$
and $\frac{2}{3}$ is subtracted from the number ....$3 x - \frac{2}{3}$
The result is $\frac{3}{4}$................................................$3 x - \frac{2}{3} = \frac{3}{4}$

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The wording of this question could be tidied up a bit. There are issues with it.

$\textcolor{b l u e}{\text{Step 1 - isolate the term with "x" in it}}$

Add $\frac{2}{3}$ to both sides turning the left hand side $- \frac{2}{3}$ into 0

color(green)(3x-2/3color(red)(+2/3)color(white)("dd")=color(white)("dd")3/4color(red)(+2/3)

$3 x + 0 = \frac{3}{4} + \frac{2}{3}$

$3 x \textcolor{w h i t e}{\text{ddd}} = \frac{3}{4} + \frac{2}{3}$
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$\textcolor{b l u e}{\text{Step 2 - simplify the right hand side}}$

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

color(green)(3x=[3/4color(red)(xx1)]+[2/3color(red)(xx1)]

color(green)(3x=[3/4color(red)(xx3/3)]+[2/3color(red)(xx4/4)]#

$3 x = \textcolor{w h i t e}{\text{dd")9/12color(white)("ddd")+color(white)("ddd")8/12color(white)("ddd}} = \frac{17}{12}$

$3 x = \frac{17}{12}$
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$\textcolor{b l u e}{\text{Step 3 - isolate } x}$

Multiply both sides by $\frac{1}{3}$ - turns the 3 from $3 x$ into 1 and $1 \times x = x$

$x = \frac{17}{12} \times \frac{1}{3} = \frac{17}{36}$

17 is a prime number so we can not simplify the fraction any further.