Question

Please help! The question is in the picture!

Answer 1

OPTION A and OPTION C

Explanation:

OPTION A:

`$ (1)/(5)x - 10 $` and
`$ (1)/(5)(x - 50) $`

Consider
`$ (1)/(5)(x - 50) = (x)/(5) - (50)/(5) $`

This is equal to
`$ (1)/(5)x - 10 $`.

This is exactly the first expression. So, we say both expressions are equivalent.

OPTION B:

`$ (1)/(3) x - 6 $` and
`$ - (1)/(3)(3x  + 18) $`

Distributing
`$ -(1)/(3) $` to
`$ (3x + 18) $` we get:

`$ (-x)/(3) + (-18)/(3) $`

⇒
`$ -x - 6`

This is not equivalent to the first expression.

OPTION C:

`$ (1)/(2)x + 8 $` and
`$ (1)/(2)(x + 16) $`

`$ (1)/(2)(x + 16) = (x)/(2) + (16)/(2) $`

`$ \implies (1)/(2)x + 8 $`

This is exactly the first expression. So, we say the expressions are equal.

We apply similar techniques to OPTION D and OPTION E. Note that the expressions are not equal in both the options.