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The multiplication property of equality is a fundamental rule in algebra that helps us solve equations. This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. The balance is crucial because it ensures the equation is still true even after the multiplication.

Imagine you're weighing two baskets on a scale, and both baskets are equal in weight. Adding or removing the same weight from both sides will not change their balance. Similarly, multiplying both sides of an equation by the same number keeps it balanced.

In the exercise provided, we are solving the equation \(-\frac{1}{5} y = -6\). By applying the multiplication property of equality, we multiply both sides by \(-5\). This step helps "clear" the fraction and makes the equation easier to solve by isolating the variable \(y\).

• The equation becomes \(y = -6 \times (-5)\).
• Keep in mind: Multiplication across the equation should not change its validity.

Solving equations is a process of finding the value(s) of the variable(s) that make the equation true. In algebra, equations often include unknown variables that you need to isolate in order to solve the equation.

The key steps in solving an equation include performing the same operation on both sides of the equation while maintaining balance. It's like a teeter-totter; any action on one side must be mirrored on the other to maintain equilibrium.

For the given problem \(-\frac{1}{5} y = -6\), we follow these basic steps:

• Identify the operation that isolates \(y\). Here, it’s multiplication by \(-5\).
• Perform the operation: Multiply \(-5\) to both sides resulting in \(y = 30\).
• After solving, verify the solution by substituting \(30\) back into the original equation to check if it maintains equality.

Solving equations often involves simplifying expressions and balancing both sides until the variable stands by itself.

Inverse operations are operations that "undo" each other. Understanding these operations is essential in algebra, especially when solving equations, because they help us isolate the variable.

Think of addition and subtraction, or multiplication and division, and how they reverse each other's effects. When solving equations, you use inverse operations to "peel away" the layers affecting the variable.

In our exercise, the equation \(-\frac{1}{5} y = -6\) uses multiplication as an inverse operation to help isolate \(y\). Since \(y\) is multiplied by \(-\frac{1}{5}\), we multiply by \(-5\) (the inverse) to cancel out the fraction.

• This action shifts the equation to a simple multiplication problem: \(y = 30\).
• Inverse operations are key tools for unbinding the variable from complex expressions.

Using inverse operations, we simplify equations and work towards finding the variable's true value, making these operations indispensable in algebra.