completely lost!! please help!

[ladydakota]

solve the following algebracially using one variable. find three consecutive even integers such that the product of the first two is two less than five times the third integer.
I'm not even sure where to start!!!

 

[Denis]

solve the following algebracially using one variable. find three consecutive even integers such that the product of the first two is two less than five times the third integer.
I'm not even sure where to start!!!

EXAMPLE: 3 consecutive even integers: 10,12,14
If we let x represent the middle one, then we have x-2, x, x+2 as the 3 integers; follow that?

 

[soroban]

Hello, ladydakota!

Solve the following algebracially using one variable.
Find three consecutive even integers such that the product of the first two is two less than five times the third integer.
I'm not even sure where to start! . Sure you do!

Name things . . .

. . \(\displaystyle \begin{array}{ccc}x &=& \text{1st integer } \\ x+2 &=& \text{2nd integer} \\ x+4 &=& \text{3rd integer} \end{array}\)


. . \(\displaystyle \underbrace{\text{product of first two }}_{x(x+2)} \underbrace{\text{ is }}_{=} \underbrace{\text{ two less than 5 times 3rd}}_{5(x+4)-2}\)


\(\displaystyle \text{There is our equation! }\quad\hdots\quad x(x+2) \;=\;5(x+4)-2\)

Edit: Um . . . too slow again!

 

[Denis]

Methinks you scared Miss Dakota away, Soroban!