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

1 Answer
Dec 30, 2015

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!