Question

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? Please explain.

Answer 1

So consecutive intergers are 1 away from each other so
the numbers are
x,x+1,x+2
if the product (multily) of 2 smaeller is 5 less than 5 times largest so
(x times (x+1)) is 5 less than 5 times (x+2)
(x times (x+1))=-5+5(x+2)
pemdas
distribute using distributiver property
a(b+c)=ab+ac so
x times (x+1)=x^2+x
5(x+2)=5x+10
we have
x^2+x=-5+5x+10
add like terms
x^2+x=5x+5
subtract (5x+5) from both sides
x^2-4x-5=0
factor by find what 2 numbers add to -4 and multply to get -5
numbers are 1 and -5
so we do
(x+1)(x-5)=0
sete each to zero
x+1=0
x-5=0

x+1=0
sbtract 1
x=-1
we want positie so thisis wrong answer

x-5=0
add 5
x=5
subsitute
x,x+1,x+2
5,5+1,5+2
5,6,7


smalles is 5