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Chapter 3: Problem 14

Solve the equation using the multiplication or division properties of equality. $$-5 y=25$$

Short Answer

Expert verified
y = -5

Step by step solution

01

Identify the equation

The given equation is \[-5y = 25\]The goal is to solve for the variable \(y\).
02

Apply the multiplication property of equality

To isolate \(y\), divide both sides of the equation by \(-5\). This is because multipling both sides by \(-\frac{1}{5}\) has the same effect.\[-5y \times \frac{1}{-5} = 25 \times \frac{1}{-5}\]
03

Simplify both sides

Simplify the equation on both sides:\[y = \frac{25}{-5}\]Doing the division, we get:\[y = -5\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication Property of Equality
The multiplication property of equality states that you can multiply both sides of an equation by the same number without changing the equality. This is useful when you need to isolate a variable. For example, in the equation \(-5y = 25\), if you multiply both sides by \(-\frac{1}{5}\), it helps in isolating \(y\). Hence, applying this property correctly allows us to simplify the equation for easier solving.
Division Property of Equality
The division property of equality is very similar to the multiplication property. It states that you can divide both sides of an equation by the same non-zero number without changing the equality. This can be extremely helpful when we need to get rid of a coefficient in front of a variable. In our example, dividing both sides of \(-5y = 25\) by \(-5\) isolates \(y\).
Isolating Variables
Isolating the variable is one of the fundamental steps in solving equations. It means manipulating the equation so that the variable is alone on one side of the equation. For instance, in \(-5y = 25\), we aimed to isolate \(y\) by using the division property. By dividing both sides by \(-5\), we achieve our goal and find that \ y = -5\. The key is to perform the same operation on both sides to maintain the equation's balance.
Negative Coefficients
Negative coefficients can make solving equations a bit tricky, but the rules remain the same. When you have a negative coefficient, like in \(-5y = 25\), you need to carefully apply the same properties of equality. By dividing both sides by \(-5\), we effectively change the negative coefficient to a positive one, making it easier to isolate \(y\). Just remember, performing any mathematical operation to both sides of an equation maintains the equality.

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Most popular questions from this chapter

Apply the appropriate property to simplify the expression. $$-8(4-p)$$

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