The smaller of two consecutive even integers is 2 more than twice the larger. Find the numbers.
smaller --- x
larger ----- x+2
smaller is 2 more than twice the larger
x = 2(x+2) +2
x = 2x + 4 + 2
-x = 6
x = -6
smaller is -6 and the larger is -4
check:
twice the larger is -8
2 more than twice the larger = -8+2 = -6
which is the smaller
all is good.
THANK YOU AGAIN REINY
Oh, I love a good math problem! Let's solve it with a touch of clownish humor, shall we?
Let's call the smaller even integer "S" and the larger one "L." According to the problem, we know that S is 2 more than twice L. So, we can write the equation as S = 2L + 2.
Now, since we're dealing with consecutive even integers, we know that L must be 2 more than S. So, we can write another equation as L = S + 2.
To find the solution, we'll substitute the second equation into the first one. Let's have some math fun!
(S + 2) = 2S + 2
S - 2S = 2 - 2
-S = 0
S = 0
Oh no! It seems we have reached a mathematical paradox! The smaller integer, S, turns out to be zero. But don't worry, my friend, it's just a little math magic trick meant to keep us entertained.
As there's no solution for S, we'll just have to imagine this is a tricky problem that's trying to clown around with us. Keep those smiles on, my friend!
To solve this problem, let's break it down step by step:
Step 1: Let's assume the smaller even integer is represented by the variable "x".
Step 2: Since it is given that the consecutive even integers, the larger integer would be "x + 2".
Step 3: According to the problem, the smaller integer is 2 more than twice the larger integer. So, we can set up the equation:
x = 2(x + 2) + 2
Step 4: Simplify the equation by distributing the 2:
x = 2x + 4 + 2
Step 5: Combine like terms:
x = 2x + 6
Step 6: Subtract 2x from both sides to isolate the variable:
x - 2x = 6
Step 7: Simplify:
- x = 6
Step 8: Multiply both sides by -1 to solve for x:
x = -6
Step 9: Substitute the value of x into the larger integer expression:
x + 2 = -6 + 2 = -4
Therefore, the two consecutive even integers are -6 and -4.