Question

What is the solution set of the equation `x/5 + x/2 =14`?

Answer 1

x=20

Explanation:

`(2x)/10 + (5x)/10 = (7x)/10 = 14`

`7x = 140`

`x = 140/7`

`x=20`

Answer 2

Virtually every step explained. Once practised you will start to use shortcut methods and jump steps (much faster).

`x=20`

Explanation:

Fraction structure:

`ubrace(color(purple)(("count")/("size indicator of what is being counted") ))color(white)("d")=color(white)("d")ubrace(color(red)( ("numerator")/("denominator")))`

`color(white)("ddd")ul("My")" description of purpose"color(white)("dddddddddd") "The proper names"`
`color(white)("dddddddddddddddddddddddddddddddddd")"that people use"`

You can only DIRECTLY add or subtract the top numbers (counts) unless the bottom numbers (size indicators) are the same.

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

`color(green)([x/5color(red)(xx1)]+[ x/2color(red)(xx1)] = 14 )`

`color(green)([x/5color(red)(xx2/2)]+[ x/2color(red)(xx5/5)] = 14 )`

`color(green)(color(white)("d")[(2x)/10]color(white)("dd")+color(white)("dd")[ (5x)/10] color(white)("d")= 14 )`

As the bottom numbers are now the same we can do this:

`color(green)((2x+5x)/10 = 14`

`color(green)((7x)/10 = 14`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Now we determine the value of "x)`

Multiply both sides by 10

`10/10xx7x=14xx10`

but `10/10=1` giving:

`7x=140`

Divide each side by 7

`7/7xx x=140/7`

We can 'split' 140 into `14xx10`

`x=(14xx10)/7`

`x=14/7xx10`

`x=2xx10=20`