Question

Ms. Johnson asked her class to write an equivalent

expression to
14d - 9 + 21k - 7dk + 2.
riley wrote the expression
7dk(2 - 3 - 1) _ 7

ahmad write the expression
7(2d + 3k - dk) - 7

Ariana wrote the expression
7k(2d - 3 - d) - 7

who is correct? explain how you know

Answer 1

Ahmad wrote the correct expression.
To prove that 7(2d + 3k - dk) - 7 is equal to 14d - 9 + 21k - 7dk + 2
Please check this solution:
7(2d + 3k - dk) - 7 = 14d - 9 + 21k - 7dk + 2
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -9 + 2
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -7

Get the common variable which is 7.
7(2d + 3k - dk) - 7 = 7(2d + 3k - dk) - 7

For checking, we can simplify the equation...
from 7(2d + 3k - dk) - 7 = 14d - 9 + 21k - 7dk + 2
We simplify it to:
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -7
7 * 2d = 14d
7 * 3k = 21k
7 * - dk = -dk

Therefore,
7(2d + 3k - dk) - 7 is equal to 14d + 21k - 7dk -7