SOLUTION: negative one-sixth of a number is less than -9 define a variable. write an inequality and solve the inequality. thank you in advance for your help

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Question 1183086: negative one-sixth of a number is less than -9 define a variable. write an inequality and solve the inequality. thank you in advance for your help
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.