Question

How do you solve `7x+6-x=6+5x-10`?

Answer 1

See a solution process below:

Explanation:

First, group and combine like terms separately on each side of the equation:

`7x + 6 - x = 6 + 5x - 10`

`7x + 6 - 1x = 6 + 5x - 10`

`7x - 1x + 6 = 6 - 10 + 5x`

`(7 - 1)x + 6 = (6 - 10) + 5x`

`6x + 6 = -4 + 5x`

Now, subtract `color(red)(6)` and `color(blue)(5x)` from each side of the equation to solve for `x` while keeping the equation balanced:

`6x + 6 - color(red)(6) - color(blue)(5x) = -4 + 5x - color(red)(6) - color(blue)(5x)`

`6x - color(blue)(5x) + 6 - color(red)(6) = -4 - color(red)(6) + 5x - color(blue)(5x)`

`(6 - color(blue)(5))x + 0 = -10 + 0`

`1x = -10`

`x = -10`

Answer 2

`x=10`

Explanation:

Simplify both sides by combing like terms:

`color(red)(7x)+color(green)(6color(red)(-x)= color(green)(6)+color(red)(5x) color(green)(-10)`

`color(red)(6x)+color(green)(6)= color(green)(-4)+color(red)(5x)`

Subtract `6` from both sides:

`color(red)(6x)+cancel(color(green)(6-6))= color(green)(-4-6)+color(red)(5x)`

`color(red)(6x)= color(green)(-10)+color(red)(5x)`

Subtract `5x` from both sides:

`color(red)(6x-5x)= color(green)(-10)+cancel(color(red)(5x-5x))`

`color(red)(x)= color(green)(-10)`

We can check our answer by substituting `-10` for `x` back into the original problem:

`7(-10)+6-(-10)=6+5(-10)-10`

`-70+6+10=6-50-10`

`-64+10=-44-10`

`-54=-54`

Indeed, our answer is correct!