Which expressions are equivalent to ? Check all that apply.

Accepted Solution

Option 1. [tex](-2)(5x) + (-2)(-\frac{3}{4})[/tex] and option 4.[tex]-10x + \frac{3}{2}[/tex] are equivalent to [tex]-2(5x-\frac{3}{4} ).[/tex]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 [tex]-\frac{3}{4}[/tex].So the expression becomes as follows;[tex]-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}).[/tex]This is the first option given so the first expression is equivalent.Step 2:[tex]-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{6}{4} = -10x + \frac{3}{2} .[/tex]Of the other four options, only the fourth expression has the fraction [tex]\frac{3}{2}[/tex] so the fourth expression is also equivalent.Expressions 1 and 4 are equivalent to the given expression.