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To solve the equation x + 2 = 2x - 6, you need to isolate x. Here's how:
1. Start by subtracting x from both sides of the equation:
x + 2 - x = 2x - x - 6
Simplifying the equation, you get:
2 = x - 6
2. Next, add 6 to both sides of the equation:
2 + 6 = x - 6 + 6
This simplifies to:
8 = x
So, the value of x is 8.
3. Since x represents the smaller even integer, the larger even integer is x + 2.
So, the larger integer is 8 + 2 = 10.
Therefore, the two consecutive even integers are 8 and 10.