To solve the equation y = 2y + 6 by inspection, we begin by isolating y on one side of the equation.
First, let’s rearrange the equation:
y – 2y = 6
This simplifies to:
-y = 6
Now, multiplying both sides by -1 gives us:
y = -6
Therefore, by inspection, a particular solution to the equation is y = -6.
This solution works because if we substitute -6 back into the original equation, we can verify:
- Left-hand side: -6
- Right-hand side: 2(-6) + 6 = -12 + 6 = -6
Both sides equal -6, confirming that our solution is correct.