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8(2q+1)=4 then 2(2q+1)=1

name the property illustrated in the equation

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You have divided both sides of the equation by 4, which is equivalent to multiplying both sides of the equation by 1/4.  Multiplying both sides of an equation by the same number is known as the multiplication property of equality.  It can be summarized as: If a = b, then a*c = b*c.