Question

How do you solve `2+6x=7+7x`?

Answer 1

`x=-5`

Explanation:

`"collect terms in x on one side of the equation and"`
`"numeric values on the other side"`

`"subtract 7x from both sides"`

`2+6x-7x=7cancel(+7x)cancel(-7x)`

`" subtracting 2 from both sides to get the numeric values"`
`"on one side"`

`rArrcancel2-cancel(2)-x=(7-2)`

`rArr-x=5`

`"multiply both sides by "-1`

`-1xx-x=-1xx5`

`rArrx=-5`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=2+(6xx-5)=2-30=-28`

`"right "=7+(7xx-5)=7-35=-28`

`rArrx=-5" is the solution"`

Answer 2

`x=-5`

Explanation:

Firstly, remember whatever we do to one side, we must do to the other.

Isolate `x` to one side by subtracting `6x`:

`2+cancel(6x)=7+x`

Isolate `x` again by cancelling out the constant `(7)` by subtracting `7`:

`-5=cancel7+x -> -5=x`