We will start our proof with the given equation.
a.&6(x-4)=42
a.&Given
Blank b.
We can justify each step to rewrite 6(x-4) as 6x-24 on the left hand side of the equation using the Distributive Property.
a(b+c)=ab+ac
After rewriting (x-4) as (x+(- 4)), we can use the Distributive Property with a=6, b=x, and c=-4. We also need to notice that 6(- 4)=- 24, and that 6x+(- 24)=6x-24.
b.&6x-24=42
b.&Distributive Property
Blank c.
According to the Addition Property of Equality, we can add a number to both sides of an equation.
Ifa=b, thena+c=b+c
In this case we add c=24 to both sides of the equation and use that 6x-24+24=6x and 42+24=66.
c.&6x=66
c.&Addition Property of Equality
Blank d.
According to the Division Property of Equality, we can divide an equation by a nonzero number.
Ifa=b and c≠0, thena/c=b/c
In this case, we divide the equation by c=6 and use that 6x6=x and 666=11.
d.&x=11
d.&Division Property of Equality
