Question

Check all the ones that are equivalent (same as): 8x - 2y + 1

A. -2y + 8x + 1.
B. 2y + 8x + 1.
C. 1 - 2y + 8x.
D. 2y - 8x + 1.

Answer 1

Options A (-2y + 8x + 1) and C (1 - 2y + 8x) are equivalent to the expression 8x - 2y + 1 because they can be rearranged without changing the value. Options B and D are not equivalent as they have different terms.

Step-by-step explanation:

To check which expressions are equivalent to 8x - 2y + 1, we need to compare each option and see if they can be rearranged to match the original expression exactly, without changing the value of the expression. Let's analyze each option:

• A. -2y + 8x + 1: This is just a rearrangement of the original expression with the terms in a different order. The commutative property of addition allows us to rearrange terms in a sum, so this expression is equivalent to 8x - 2y + 1.
• B. 2y + 8x + 1: This expression has a positive 2y instead of a negative 2y, so it is not equivalent to 8x - 2y + 1.
• C. 1 - 2y + 8x: This is another rearrangement of the original expression, which is also equivalent by the commutative property of addition.
• D. 2y - 8x + 1: Similar to option B, this has a positive 2y and the x term has changed sign as well, so it is not equivalent to the original expression.

Therefore, options A and C are equivalent to the original expression 8x - 2y + 1.