Question

How do you solve `9x < 9( 1- x )`?

Answer 1

`x < 1/2`

Explanation:

First, you need to expand the terms within parenthesis:

`9x < (9 xx 1) - (9 xx x)`

`9x < 9 - 9x`

Next we can isolate the `x` terms on one side of the inequality and the constants on the other by using the necessary arithmetic while keeping the inequality balanced:

`9x + color(red)(9x) < 9 - 9x + color(red)(9x)`

`(9 + 9)x < 9 + (-9 + 9)x`

`18x < 9 + 0x`

`18x < 9 + 0`

`18x < 9`

Finally, we can solve for `x` while keeping the inequality balanced:

`(18x)/color(red)(18) < 9/color(red)(18)`

`(color(red)(cancel(color(black)(18)))x)/color(red)(cancel(color(black)(18))) <1/2`

`x < 1/2`