Question

How do you solve `7/5x+3/5= -x`?

Answer 1

`x = -1/4`

Explanation:

`7/5.x+3/5=−x`

Let us write "`-x`" otherwise :

<=> `7/5.x+3/5=−5/5.x`

If we add the same value to each side, we maintain the equality :

<=> `7/5.x+3/5 color(red)+ color(red)(5/5.x)=−5/5.x color(red)+ color(red)(5/5.x)`

Add together fractions with a unknown & with the same denominator :

<=>`color(green)(7/5.x)+3/5 + color(green)(5/5.x)=0`

<=>`color(green)(12/5.x)+3/5=0`

Substract -3/5 to each member of equality :

<=>`12/5.x=-3/5`

Multiply by 5 each side :

<=>`12x = -3`

<=>`x = -3/12`

<=>`x = -1/4`

Note : You can start with a multiplication :

`7/5.x+3/5=−x` <=> `7x+3=−5x`
but I like to complicate my life. ;)