Question

Which expressions are equivalent to_____? Check all that apply.

Answer 1

Option 1. $(-2)(5x) + (-2)(-\frac{3}{4})$ and option 4.$-10x + \frac{3}{2}$ are equivalent to $-2(5x-\frac{3}{4} ).$

Step-by-step 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 $-\frac{3}{4}$.

So the expression becomes as follows;

$-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}).$

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

Step 2:

$-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{6}{4} = -10x + \frac{3}{2} .$

Of the other four options, only the fourth expression has the fraction $\frac{3}{2}$ so the fourth expression is also equivalent.

Expressions 1 and 4 are equivalent to the given expression.