Question

Give reasons for each step of the deductive argument that if x – 5 = 2(x + 6), then x = -17.
x – 5 = 2(x + 6) Original problem
x – 5 = 2x + 12 1)
-5 = x + 12 2)
-17 = x 3)
x = -17 4)
Answer choices:
Reflexive property
Symmetric property
Transitive property
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Substitution property
Distributive property

Answer 1

x - 5 = 2(x + 6) --- original problem
x - 5 = 2x + 12 --- distributive property
-5 = x + 12 -- result of subtracting x ...subtraction property of equality
-17 = x -- result of subtracting 12...subtraction property
x = -17 -- result of multiplying by -1 ...multiplication property......or I guess it could be reflexive property...not 100% sure.

Answer 2

Thanks, that was helpful!