Question

How do you solve `-\frac { 2} { 5} x + 3= \frac { 2} { 3} x + \frac { 1} { 3}`?

Answer 1

Showing first principle method in detail. Once you are used to this approach start using shortcuts. They are very much faster.

`x=5/2`

Explanation:

`color(blue)("Method:")`

`color(brown)("Step 1:")`
Manipulate the equation so that you have collected all the terms with `x` in them on one side of the equals and everything else on the other side.

`color(brown)("Step 2:")`
Manipulate the equation so that you only have 1 `x` and for that to be on its own on one side of the equals and everything else on the other side.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "-2/5x+3=2/3x+1/3`

`color(green)("Step 1")`
The `2/3x` is positive so move the `-2/5x` to the other side so that all our `x` terms are positive.#

Add `color(blue)(2/5x)`to both sides

`color(brown)(-2/5xcolor(blue)(+2/5x)+3" "=" "2/3xcolor(blue)(+2/5x)+1/3)`

`" "0+3" "=" "2/3x+2/5x+1/3`

Subtract `1/3` from both sides

`" "3-1/3" "=" "2/3x+2/5x+0`

`" "8/3" "=" "16/15x`
...............................................................................................................

`color(green)("Step 2")`

Multiply both sides by`15/16`. This turns `16/15 x" into "1xx x->x`

`8/3xx15/16=x`

This is the same as:

`8/16xx15/3=x`

`1/2xx5=x`

`x=5/2`