Q2. - Algebra 2

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.

Step-by-Step Solution

Answer

The required answer is Always true.

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.

Step 2 – 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.