Solve by using the multiplication principle. \( 5 x=-10 \) Choose the correct definition of the multiplication principle. A. \( b=c \) is equivalent to \( b \cdot c=a \). B. \( a=b \) is equivalent to \( b \cdot a=c \). C. \( a=b \) is equivalent to \( a \cdot c=b \cdot c \). D. \( b=c \) is equivalent to \( a \cdot c=b \cdot c \).

To solve the equation \( 5x = -10 \) using the multiplication principle, we can isolate \( x \) by dividing both sides by 5. This gives us \( x = \frac{-10}{5} \), resulting in \( x = -2 \). Therefore, the correct application of the multiplication principle allows us to manipulate equations by multiplying or dividing both sides by the same non-zero number to maintain equality. The correct definition of the multiplication principle is C. \( a = b \) is equivalent to \( a \cdot c = b \cdot c \). This principle is super useful because it enables you to maintain the equality of an equation while simplifying or solving for unknown variables. Just remember to apply it carefully, as dividing by zero will lead you astray!