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When working with linear equations, combining like terms is an essential skill. This step involves simplifying expressions by merging terms that have the same variable part or power. In the original exercise, you have two terms, \( y \) and \(-6y \), on the left side of the equation.

These terms are considered 'like' because they both contain the variable \( y \). To combine them, think of it as adding or subtracting the coefficients (the numbers in front of the variables) while keeping the variable part unchanged:

• Coefficient of \( y \) is 1.
• Coefficient of \(-6y \) is -6.

Add these coefficients:
\( 1 - 6 = -5 \)
Thus, the expression becomes \(-5y \).

By doing this, you transform the original equation into something simpler and easier to handle. Understanding how to combine like terms efficiently will help simplify more complex algebraic equations in the future!

Simplifying expressions assists in making equations more manageable before solving them. It involves reducing the equation to its most straightforward form by performing arithmetic operations and merging like terms.

In the case of the original exercise, simplifying occurred as the left side reduced from \( y - 6y \) to \( -5y \).
This step involves a couple of arithmetic operations, as discussed:

• Recognize and group like terms.
• Perform any necessary subtraction or addition, as seen with the coefficients of \( y \) and \(-6y \).

After simplification, you're left with an equation that shows the clear relationship between the variable and constants, here \(-5y = 20\). This transformation makes the next steps toward solving the equation straightforward.

Solving equations often requires isolating the variable on one side, which sometimes involves using division. Division in linear equations is crucial because it allows you to isolate the variable, making it possible to find its value.

In the original exercise, once we've simplified to \(-5y = 20\), we need to solve for \( y \). To do that, follow these steps:

• Divide each side of the equation by the coefficient of \( y \), which is \(-5\).
• Write: \( y = \frac{20}{-5} \).

This is how you isolate \( y \) on one side, while solving for its value on the other side.

Performing the division yields \( y = -4 \), providing the solution to the equation. Mastering how to use division effectively in equations will help solve various types of algebraic problems, especially in cases where isolating the variable is necessary.