Question

Which expression is equivalent to the expression below? Select all that apply. –2/5(15 – 20d + 5c) A. –30 + 40d – 10c B. –6 + 8d – 2c C. –2c + 8d – 6 D. 6 – 8d + 2c

Answer 1

Answer:

B. -6+8d-2c  C. -2c+8d-6

Step-by-step explanation:

In order to determine which expressions are equivalent to $-\frac{2}{5} (15-20d+5c)$ you need to set the expression equal to the options available.

For example, to check if A. works:

$-\frac{2}{5}(15-20d+5c)=-30+40d-10c\\\\\Multiply (-2/5) to the other side:\\15-20d+5c=(-5/2)(-30+40d-10c)\\Cancel out common factors and distribute:\\15-20d+5c= -5(-15+20d-5c)\\15-20d+5c= 75-100d+25c\\\\Solve:\\60-80d+20c \neq -\frac{2}{5} (15-20d+5c)$

You want to repeat the process as shown above with the rest of the options. If both sides equal to each other, once solved, that means that will be the answer.