Question

Which expressions are equivalent to_____? Check all that apply.

Answer 1

Option 1.
`(-2)(5x) + (-2)(-(3)/(4))` and option 4.
`-10x + (3)/(2)` are equivalent to
`-2(5x-(3)/(4) ).`

Explanation:

Step 1:

The given expression is expanded as follows.

The -2 is multiplied with the 5x and then the -2 is multiplied with the
`-(3)/(4)`.

So the expression becomes as follows;

`-2(5x-(3)/(4) ) = (-2)(5x) + (-2)(-(3)/(4)).`

This is the first option given so the first expression is equivalent.

Step 2:

`-2(5x-(3)/(4) ) = (-2)(5x) + (-2)(-(3)/(4)) = -10x + (6)/(4) = -10x + (3)/(2) .`

Of the other four options, only the fourth expression has the fraction
`(3)/(2)` so the fourth expression is also equivalent.

Expressions 1 and 4 are equivalent to the given expression.