Question

Given the inequality 5(n − 4) < 4(n + 15), determine which integer makes the inequality false.

S:{80}
S:{15}
S:{5}
S:{−9}

1. bonexptip
-9
Step-by-step explanation:
5(-9-4)
5(-13)
-65
4(-9+15)
4(6)
24
-65<24 so -9 is false because -65 is not smaller than 24

2. The solution is Option A.
The value of n which makes the inequality 5 ( n − 4 ) < 4 ( n + 15 ) false is when n = 80
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is given by
5 ( n − 4 ) < 4 ( n + 15 )
Now , on substituting the value of n as 80 in the inequality equation , we get
5 ( n − 4 ) < 4 ( n + 15 )
when n = 80
5 ( 80 – 4 ) < 4 ( 80 + 15 )
5 ( 76 ) < 4 ( 95 )
380 = 380
So , the inequality will become false as the two sides of the equation will result in value 380 when n = 80
Hence ,
The value of n = 80 in the inequality equation 5 ( n − 4 ) < 4 ( n + 15 ) will make it false