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When solving equations in prealgebra, a crucial step is to isolate the variable. This means getting the variable you are solving for by itself on one side of the equation. Let's break down how you would do this.

Consider the equation \( \frac{y}{5} = -8 \). Here, \( y \) is our variable, and we need to isolate it to find its value.

To remove the fraction, multiply both sides by the number in the denominator, which is 5 in this case. This allows the fraction to "cancel out". So, multiply both sides by 5:

• Equation: \( 5 \times \frac{y}{5} = 5 \times -8 \)
• Left side: \( y \) (The 5 in the numerator and denominator cancel out)
• Right side: \( -40 \)

This simplifies to \( y = -40 \). Now, the variable is isolated, and we have our solution.

After isolating the variable and finding a solution, it’s essential to check if this solution is correct. This verification step ensures that no mistakes have been made in your calculations. To do this, substitute your solution back into the original equation.

Let's apply this to our problem. You found that \( y = -40 \) from isolating the variable. Now, plug \( y = -40 \) back into the original equation \( \frac{y}{5} = -8 \) to check it:

• Substitute \( y = -40 \) into \( \frac{y}{5} \)
• Calculate: \( \frac{-40}{5} = -8 \)
• Simplify: \( -8 = -8 \)

The equation holds true, confirming that \( y = -40 \) is indeed the correct solution. Checking your work helps build confidence and ensures accuracy.

Prealgebra is often the foundational stage in learning mathematics, focusing on basic arithmetic and the introduction to algebraic concepts. It's an essential step for students to become comfortable with handling equations, like in the example provided.

In prealgebra, you'll learn to deal with numbers and basic operations, setting the stage for algebra. Some core skills include:

• Understanding and manipulating fractions
• Working with negative numbers
• Learning to balance equations
• Gaining familiarity with variables

The exercise of solving \( \frac{y}{5} = -8 \) uses all of these skills by requiring you to balance an equation and work with fractions and negative numbers. Mastery at this level lays down the groundwork for more advanced math courses and problem-solving skills, which are crucial in many real-life applications.