Final answer:
To find the missing number in the equation that has no solutions, we can simplify the equation and manipulate it to reach a contradiction.
Step-by-step explanation:
To find the missing number so that the equation has no solutions, we need to simplify the equation and manipulate it in a way that leads to a contradiction. Let's start by distributing the 2:
x + 6 = -6x + 2 + x - 16
Combining like terms:
x + 6 = -5x - 14
Add 5x to both sides:
6x + 6 = -14
Subtract 6 from both sides:
6x = -20
Divide both sides by 6:
x = -rac{20}{6}
So the missing number is -rac{20}{6} or -rac{10}{3}. Plugging this value back into the equation would result in a contradiction because it would lead to an inequality such as 1 = -9.
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