Question

How do you solve `5x - 5= 2( x + 1) + 3x - 7`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`5x - 5 = color(red)(2)(x + 1) + 3x - 7`

`5x - 5 = (color(red)(2) xx x) + (color(red)(2) xx 1) + 3x - 7`

`5x - 5 = 2x + 1 + 3x - 7`

Next, group and combine like terms on the right side of the equation:

`5x - 5 = 2x + 3x + 1 - 7`

`5x - 5 = (2 + 3)x + (1 - 7)`

`5x - 5 = 5x + (-6)`

`5x - 5 = 5x - 6`

Next, subtract `color(red)(5x)` from each side of the equation:

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

`0 - 5 = 0 - 6`

`-5 != -6`

Because `-5` is obviously not equal to `-6` there is no solution for this problem. Or, the solution is the empty or null set: `{O/}`