Question

How do you solve `8(x + 1)> 7(x + 2)`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms within parenthesis on both sides of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(8)(x + 1) > color(blue)(7)(x + 2)`

`(color(red)(8) xx x) + (color(red)(8) xx 1) > (color(blue)(7) xx x) + (color(blue)(7) xx 2)`

`8x + 8 > 7x + 14`

Now, subtract `color(red)(8)` and `color(blue)(7x)` from each side of the inequality to solve for `x` while keeping the inequality balanced:

`-color(blue)(7x) + 8x + 8 - color(red)(8) > -color(blue)(7x) + 7x + 14 - color(red)(8)`

`(-color(blue)(7) + 8)x + 0 > 0 + 6`

`1x > 6`

`x > 6`