The greater of two consecutive even integers is six less than twice the smaller. Find the integers.
The greater of two consecutive even integers is six less than twice the smaller. Find the integers
How about x + 2 = 2x - 6
almost .. it's x + (x+2)=2x-2
To solve this problem, let's assign variables to the integers. Let x be the smaller even integer.
According to the problem, the greater even integer is six less than twice the smaller. So, the greater integer can be represented as: 2x - 6.
Since we know that the two integers are consecutive, we can express the next even integer as x + 2.
Now, we can set up the equation based on the given information:
x + 2 = 2x - 6
To solve the equation, we will isolate x:
x - 2x = -6 - 2
Simplifying:
-x = -8
Dividing both sides by -1, the coefficient of x:
x = 8
Therefore, the smaller even integer is 8, and the greater even integer is the next consecutive even number, which is 8 + 2 = 10.
So, the two integers are 8 and 10.
To solve the problem, we need to set up an equation that represents the given information. Let's call the smaller integer x. Since the problem states that the greater integer is six less than twice the smaller, we can write the equation as follows:
x + (x + 2) = 2x - 6
Now, let's solve for x:
Combining like terms:
2x + 2 = 2x - 6
Subtract 2x from both sides to isolate the constant terms:
2 = -6
Obviously, this equation is not possible.
Therefore, there must be an error in the problem statement.