Question

Which are equivalent expressions?

Answer 1

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).