Question

Question #a3e2c

Answer 1

`x = 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 = 3x`

Subtracting `2/3` from that `= 3x - 2/3`

The result is `3/4`, so

`3x - 2/3 = 3/4`

We can then solve our equation:

`3x - 2/3 = 3/4`

Add `2/3` to both sides:

`3x = 3/4 + 2/3`

`3x = 17/12`

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

`x = 17/36`

You can then check your answer (optional):

`17/36 * 3 = 17/12`

`17/12 - 2/3 = 3/4`

Answer 2

`17/36`

Explanation:

Breaking the question down into its component parts.

A number ......................................................... `x`
is multiplied by 3 ...........................................`3x`
and `2/3` is subtracted from the number ....`3x-2/3`
The result is `3/4`................................................`3x-2/3=3/4`

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

`color(blue)("Step 1 - isolate the term with "x" in it")`

Add `2/3` to both sides turning the left hand side `-2/3` into 0

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

`3x+0=3/4+2/3`

`3xcolor(white)("ddd")=3/4+2/3`
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`color(blue)("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)]`

`3x=color(white)("dd")9/12color(white)("ddd")+color(white)("ddd")8/12color(white)("ddd") = 17/12`

`3x=17/12`
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`color(blue)("Step 3 - isolate "x)`

Multiply both sides by `1/3` - turns the 3 from `3x` into 1 and `1xx x= x`

`x=17/12xx1/3 = 17/36`

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