Final answer:
The property that justifies the equation is the distributive property. You can solve this equation by applying the distributive property and then isolating the variable.
Step-by-step explanation:
The property that justifies the equation 7[6-2a] = 5[-3a+1] is the distributive property.
The distributive property states that for any numbers a, b, and c, a(b+c) = ab + ac. In this case, we can apply the distributive property to both sides of the equation:
7(6-2a) = 5(-3a+1)
42 - 14a = -15a + 5
Now, we can solve for 'a' by combining like terms and isolating the variable:
-14a + 15a = 5 - 42
a = -37