Question

The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.

If x represents the smallest integer, then which of the following equations could be used to solve the problem?
Ox= 2x + 6
Ox= 2x + 3
2x + 2 = x + 4

Answer 1

x=2x+6 is the equation that to solve for the smallest.

The three numbers are -6, -4 , and -2.

Explanation:

Let x be the smallest of three consecutive even integers.

The next even integer would then have to be x+2 (because x+1 is odd if x is even).

The third one in this sequence would have to be x+4 (because x+3 is odd if x is even).

We are given the first of these numbers equals the sum of the second and third.

So we have x=(x+2)+(x+4).

Combine like terms on right hand side:

x=x+x+2+4

Simplify the combining:

x=2x+6

Subtract 2x on both sides:

x-2x=6

Simplify left hand side:

-x=6

Multiply both sides by -1:

x=-6

If x=-6, then the three mentioned numbers are:

x=-6

x+2=-6+2=-4

x+4=-6+4=-2

The three numbers are -6, -4 , and -2.