Question

Determine whether the following statement is sometimes, always, or never true. Explain.

Dividing each side of an equation by the same expression produces an equivalent equation.

Short answer

The required answer is Always true.

Step-by-step solution

Step 1- Observe the provided statement

Dividing, multiplying, addition and subtraction with the same expression or number on both sides of any equation will not affect the equality of that equation.

– Provide an example

Take an equation $7x=-14$and perform division of 7 on both the sides.

$$\begin{gathered} \frac{7x}{7}=-\frac{14}{7} \\ x=-7 \end{gathered}$$

Step 3- Make the conclusion

As the resulting equation has equal values on both the sides which means that the provided statement is always true.