Question

Determine whether 3x +12 + x is equivalent to 4(3 + x). Use properties of order of operations to justify your answer.

Answer 1

The equations are equivalent: both results are x= -3

Proof:
3x +12 + xSolve for x:
4 (x + 3) = 0
Divide both sides of 4 (x + 3) = 0 by 4:
(4 (x + 3))/4 = 0/4
4/4 = 1:
x + 3 = 0/4
0/4 = 0:
x + 3 = 0
Subtract 3 from both sides:
x + (3 - 3) = -3
3 - 3 = 0:
Answer: x = -3

Second operation:
4(3 + x)Solve for x:
4 (x + 3) = 0
Divide both sides of 4 (x + 3) = 0 by 4:
(4 (x + 3))/4 = 0/4
4/4 = 1:
x + 3 = 0/4
0/4 = 0:
x + 3 = 0
Subtract 3 from both sides:
x + (3 - 3) = -3
3 - 3 = 0:
Answer: x = -3

Answer 2

Hello there!

3x + 12 + x

4x + 12

Let solve the second one

4(3 + x)

Distributive property

(4)(3) + (4)(x)

12 + 4x

Since we always the one with the variable leads, we change them side.

4x + 12


Thus, they are equivalent!