Question

Which expressions are equivalent to z+(z+6)?

Choose all answers that apply:
a. (z+z)+(z+6)
b. (z+6)+6
c. 2(z+3)

Answer 1

The equivalent expression to z + (z + 6) is option c. 2(z + 3), which upon distribution results in 2z + 6, the same as adding z to z and then 6.

Step-by-step explanation:

To find equivalent expressions for z + (z + 6), we can simplify or re-write the expression using the associative and distributive properties of addition and multiplication in different ways. Let's consider each of the given options:

• a. (z + z) + (z + 6): Using the associative property (A + B = B + A), we can regroup the terms without changing their sum. Therefore, (z + z) + (z + 6) simplifies to 2z + (z + 6), which is just z + z + z + 6 or 3z + 6, which is not the same as z + (z + 6).
• b. (z + 6) + 6: This is simply adding 6 twice to z, and there's no z being added twice, so it is not equivalent to z + (z + 6).
• c. 2(z + 3): Distributing the 2 gives us 2z + 6, which is exactly z added to z and then 6 added after, so it is equivalent to z + (z + 6).

Thus, the equivalent expression to z + (z + 6) is c. 2(z + 3).