Question 328694
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.