91Ó°ÊÓ

Understanding inverse operations is key in algebra, especially when solving equations. Operations such as addition, subtraction, multiplication, and division have corresponding inverse operations that essentially "undo" them. When you think of a seesaw, inverse operations act like balancing weights.

In this exercise, we encounter

• Operation: multiplication by -1 (negative sign before the variable).
• Inverse Operation: multiplication by -1 again to reverse the effect.

To isolate a variable, we use inverse operations to bring the variable to one side of the equation while maintaining equal balance on both sides. It's much like removing weights to balance the seesaw again.

Therefore, applying the inverse of multiplying by -1 to (-w) = (-7) allows us to extract w by making the coefficient positive, simplifying the solution process.

Equation solving is the process of finding the value of a variable that turns an equation into a true statement. Here, the goal was to find the value of "w" that satisfies the equation (-w = -7).

The solution involved:

• Identifying the operation affecting the variable (a negative sign indicating multiplication by -1).
• Applying the inverse operation (multiplying both sides by -1) to isolate the variable "w".

By executing these steps carefully, we ensure that the solution comprehensively addresses both sides of the equation equally.
This process not only finds the answer but strengthens our understanding of how operations and their inverses work in tandem to maintain balance within algebraic equations.

Once we solve for a variable in an equation, it's important to double-check our solution. This verification step ensures there are no errors, confirming that the solution truly satisfies the original equation.

To "check" involves substituting the found value back into the initial equation. In our case:

• Insert the solution, which is 7, for "w" back into the equation: (- (7) = -7) .
• Compute to see if both sides match: (-7) = (-7).

The sides matched in this instance, showing our work was done correctly.
Checking solutions not only reassures accuracy but also builds confidence in our ability to solve equations methodically.