SOLUTION: five times the lesser of two consecutive even integers is at most four times the greatergreater.What are the possible values of the integers?

Question 1144251: five times the lesser of two consecutive even integers is at most four times the greatergreater.What are the possible values of the integers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let the two consecutive even integers be equal to x and x + 2.
your equation becomes 5x <= 4 * (x + 2)
simplify to get:
5x <= 4x + 8
solve for x to get:
x <= 8

this means that x has to be either:
8 or 6 or 4 or 2 or 0 or -2 or -4 .....

this also means that x cannot be greater than 8, which means that x cannot be either:
10 or 12 or 12 or 16 or 18 .........

when x = 8, the equation becomes 5 * 8 <= 4 * 10 which becomes 40 <= 40 which is true.

when x = 6, which is smaller than 8, the equation becomes 5 * 6 <= 4 * 8 which becomes 30 <= 32 which is true.

when x = 10, which is greater than 8, the equation becomes 5 * 10 <= 4 * 12 which becomes 50 <= 48 which is false.

you can graph this by breaking it up into two equations as listed below.
y = 5 * x
y = 4 * (x + 2)

you graph both these equations on the same graph as shown below.

$$$

the red line is the graph of the equation y = 5x.
the blue line is the graph of the equation y = 4 * (x + 2).

you can see that the red line is below the blue line up until the value of x is equal to 8, after which it is above the blue line.

this visually confirms the fact that 5x <= 4 * (x + 2) when the value of x is less than or equal to 8.

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