SOLUTION: Our integer is 6 less than another integer. The product of the lesser integer and -7 is 42 more than the greater integer. What are the integers?

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Question 633493: Our integer is 6 less than another integer. The product of the lesser integer and -7 is 42 more than the greater integer. What are the integers?
Found 2 solutions by MathLover1, ankor@dixie-net.com:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
remember: An integer is a whole number (not a fraction) that can be positive, negative, or zero.

let’s integers be x and y......the lesser integer, our integer is x
and the greater integer is y
given:
x%2B6=y............1
if the product of the lesser integer x and -7+is 42 more
than the greater integer y, than we have
x%28-7%29=y%2B42........2
solve this system
x%2B6=y............1....substitute y in 2
x%28-7%29=y%2B42........2
-----------------------------------
x%28-7%29=%28x%2B6%29%2B42........2.....solve for x
-7x=x%2B6%2B42
-7x-x=48
-8x=48
x=48%2F%28-8%29
x=-6
now, find y
x%2B6=y............1..plug in x=-6
-6%2B6=y
0=y
so, the integers are:x=-6 and y=0

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = our integer
then
(x+6) = another integer
:
Write an equation for the statement:
:
" The product of the lesser integer and -7 is 42 more than the greater integer"
-7x = (x+6) + 42
-7x - x = 48
-8x = 48
x = 48%28-8%29
x = -6 is the lesser integer
then
-6 + 6 = 0 is greater integer
:
Check solution in the given statement:
-7(-6) = 0 + 42