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Question 328694: what is the answer for 9 less than the product of a number and -4 is greater than 7?
Found 4 solutions by rapaljer, nyc_function, mananth, Theo:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let x=the number
Start with "the product of the number and -4", which is -4x. Then take 9 less than this:
-4x-9>7
Now, solve the inequality by adding +9 to each side:
-4x-9+9>7+9
-4x>16
Finally, divide both sides by -4. Remember, when you divide both sides of an inequality by a NEGATIVE number, you must REVERSE the inequality!!
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Answer by nyc_function(2741)  (Show Source):
Answer by mananth(16946)  (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! to begin with, let the number be x.
the product of the number and -4 is equal to -4*x.
9 less than that is equal to -4*x - 9
the whole thing is greater than 7 becomes:
-4*x - 9 > 7
add 9 to both sides of this equation to get:
-4*x > 16
divide both sides of this equation by 4 to get:
-x > 4
multiply both sides of this equation by -1 to get:
x < -4
The multiplication of both sides of an inequality by a negative number reverses the inequality.
You can test your answer by substituting in the original equation.
If x is smaller than -4, then the equation should be true.
If x is equal to or greater than -4, then the equation should be false.
We'll work from the original statement rather than the original equation.
They should both be equivalent if we translated the statement to the equation correctly,.
the original statement is:
what is the answer for 9 less than the product of a number and -4 is greater than 7?
when x = -5, this statement becomes:
what is the answer for 9 less than the product of -5 and -4 is greater than 7
product of -5 and -4 = 20
9 less than that = 11
11 is greater than 7 so we're good.
we'll next try x = -4
product of -4 and -4 = 16
9 less than that = 7
7 is NOT greater than 7 so we're good because x had to be less than -4, not equal to it.
we'll next try x = -3
product of -4 and -3 = 12
9 less than 12 = 3
3 is NOT greater than 7 so we're good because x had to be less than -4, not greater than it.
Your answer is that x has to be smaller than -4.
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