Question

Please help! The question is in the picture!

Answer 1

Answer:

OPTION A and OPTION C

Step-by-step explanation:

OPTION A:

$\frac{1}{5}x - 10$ and $\frac{1}{5}(x - 50)$

Consider $\frac{1}{5}(x - 50) = \frac{x}{5} - \frac{50}{5}$

This is equal to $\frac{1}{5}x - 10$.

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

OPTION B:

$\frac{1}{3} x - 6$ and $- \frac{1}{3}(3x + 18)$

Distributing $-\frac{1}{3}$ to $(3x + 18)$ we get:

$\frac{-x}{3} + \frac{-18}{3}$

⇒ $-x - 6$

This is not equivalent to the first expression.

OPTION C:

$\frac{1}{2}x + 8$ and $\frac{1}{2}(x + 16)$

$\frac{1}{2}(x + 16) = \frac{x}{2} + \frac{16}{2}$

$\implies \frac{1}{2}x + 8$

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.