Question

How do you solve the inequality `–9(x – 2) < –72`?

Answer 1

S = `( x in RR | x > 10)`

Explanation:

`-9` multiplies the parenthesis content, so:
`-9 * x + (-9) * -(2)`
`-9x + 18 < -72`.

`18` passes to the other side and changes it sign:

`-9x < -72 - 18`

`-9x < -90`

Now, `-9` that multiplies `x` passes to the other side, dividing `-90`:

`x > (-90)/(-9)`

Notice that the direction of inequality has changed because either side was divided by a negative number.

Double negative equals positive, and `90/9 = 10`, and the sense
of direction changes because as a rule if a negative number is multiplied or divided to both sides of an inequality the sense of direction changes.
`x >10`.

Solution set: S = `( x in RR | x > 10)`.

This can be checked by substituting any number greater than positive 10 into the original inequality, say 11, and we have

`-9(11-2) = -81 < -72`

which is true!