Question

Is the inequality `-2(2x+9) > -4x+9` sometimes, always, or never true?

Answer 1

See a solution process below:

Explanation:

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

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

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

`-4x - 18 > -4x + 9`

Now, add `color(4x)` to each side of the inequality:

`color(4x) - 4x - 18 > color(4x) - 4x + 9`

`0 - 18 > 0 + 9`

`-18 > 9`

Because this inequality is not try, `-18` is actually less than `9`, then this inequality is never true.