Question

How do you solve `-3( 8x + 9) > - 27- 24x`?

Answer 1

See a solution process below:

Explanation:

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

`color(red)(-3)(8x + 9) > -27 - 24x`

`(color(red)(-3) xx 8x) + (color(red)(-3) xx 9) > -27 - 24x`

`-24x + (-27) > -27 - 24x`

`-24x - 27 > -27 - 24x`

Add `color(red)(24x)` and `color(blue)(27)` to each side of the inequality:

`color(red)(24x) - 24x - 27 + color(blue)(27) > color(blue)(27) - 27 - 24x + color(red)(24x)`

`0 - 0 > 0 - 0`

`0 > 0`

Because this inequality is false there is no solution to this problem. Or, the solution is the null or empty set: `{O/}`

However, if the inequality was:

`0 >= 0`

Then this is a true statement and the solution set would the the set of all Real Numbers or: `{RR}`