Answer:
B) 4x + 8y = 2(2x + 4y)
C) 4x + 8y = 4(x + 2y)
D) 4x + 8y + 12z = 4(x + 2y + 3z)
E) 5x + 10y = 5(x + 2y)
Step-by-step explanation:
We would assume a value for the variables a, b, c, x, y and z.
Let x, a = 1
Let y, b = 2
Let z, c = 3
A) a + b + c = 3abc
When a = 1, b = 2 and c = 3
Substituting into the above equation, we have;
1 + 2 + 3 = 3(1*2*3)
6 ≠ 3(6)
6 ≠ 18 (not equivalent)
B) 4x + 8y = 2(2x + 4y)
When x = 1 and y = 2
Substituting into the above equation, we have;
4(1) + 8(2) = 2(2*1 + 4*2)
4 + 16 = 2(2 + 8)
20 = 2(10)
20 = 20 (equivalent expression)
C) 4x + 8y = 4(x + 2y)
When x = 1 and y = 2
Substituting into the above equation, we have;
4(1) + 8(2) = 4(1 + 2*2)
4 + 16 = 4(1 + 4)
20 = 4(5)
20 = 20 (equivalent expression).
D) 4x + 8y + 12z = 4(x + 2y + 3z)
When x = 1, y = 2 and z = 3
Substituting into the above equation, we have;
4(1) + 8(2) + 12(3) = 4(1 + 2*2 + 3*3)
4 + 16 + 36 = 4(1 + 4 + 9)
56 = 4(14)
56 = 56 (equivalent expression).
E) 5x + 10y = 5(x + 2y)
When x = 1 and y = 2
Substituting into the above equation, we have;
5(1) + 10(2) = 5(1 + 2*2)
5 + 20 = 5(1 + 4)
25 = 5(5)
25 = 25 (equivalent expression).
