Question 1183086
the inequality is:


-1/6 * x < -9


multiply both sides of the inequality by -1 to get:


1/6 * x > 9


multiplying both sides of an inequality by a negative number reverses the inequality.
that's what happened above when we multiplied both sides of the inequality by -1.


the inequality becomes 1/6 * x > 9
multiply both sides of the inequality by 6 to get:
x > 9 * 6 which becomes:
x > 54.


if x is greater than 54, the inequality is true.
if x is equal to or less than 54, the inequality is false.


take x = 60 which is greater than 54.
the inequality becomes:
-1/6 * 60 < -9 which becomes -10 < -9 which is true.


take x = 54 which is equal to 54.
the inequality becomes:
-1/6 * 54 < -9 which becomes -9 < -9 which is false.


take x = 48 which is less than 54.
the inequality becomes:
-1/6 * 48 < -9 which becomes -8 < -9 which is false.


this confirms that the inequality is true only if x > 54.