tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer.what are the integers?
3(x+2) = x-10
3x+6 = x-10
2x = -16
x = -8
the numbers are -8 and -6
check:
3 * -6 = -18
-8 - 10 = -18
To solve this problem, let's set up equations based on the given information.
Let's assume that the first consecutive even integer is x. Since it's an even integer, the next consecutive even integer would be (x + 2).
According to the problem, tripling the greater integer is the same as subtracting 10 from the lesser integer. So, we can write the following equation:
3(x + 2) = x - 10
Now, let's solve this equation step by step:
Expanding the left side of the equation:
3x + 6 = x - 10
Moving all the x terms to the left side and the constant terms to the right side:
3x - x = -10 - 6
2x = -16
Dividing both sides of the equation by 2:
x = -8
So, the first even integer is -8, and the next consecutive even integer would be (-8 + 2) = -6.
Therefore, the two integers are -8 and -6.