Question

How do you solve `2( 9- x ) > 4x + 9`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(2)(9 - x) > 4x + 9`

`(color(red)(2) xx 9) - (color(red)(2) xx x) > 4x + 9`

`18 - 2x > 4x + 9`

Next, add `color(red)(2x)` and subtract `color(blue)(9)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`18 - color(blue)(9) - 2x + color(red)(2x) > 4x + color(red)(2x) + 9 - color(blue)(9)`

`9 - 0 > (4 + color(red)(2))x + 0`

`9 > 6x`

Now, divide each side of the inequality by `color(red)(6)` to solve for `x` while keeping the inequality balanced:

`9/color(red)(6) > (6x)/color(red)(6)`

`(3 xx 3)/color(red)(3 xx 2) > (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6))`

`(color(red)(cancel(color(black)(3))) xx 3)/color(red)(color(black)(cancel(color(red)(3))) xx 2) > x`

`3/2 > x`

We can reverse or "flip: the entire inequality to state the solution in terms of `x`:

`x < 3/2`