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Solving equations is a fundamental skill in algebra. The goal is to find the value of the variable that makes the equation true. It's often like solving a puzzle where you manipulate the equation to get the unknown variable by itself on one side. This process typically involves several steps, including simplifying terms, moving terms from one side of the equation to the other, and sometimes factoring or using specific formulas. When solving an equation, always ensure that the operations you perform on one side are also done to the other to maintain equality and balance the equation properly.

Like terms are terms within an algebraic expression that have identical variable parts raised to the same power. In the equation from the exercise, you encounter terms like \(2y\) and \(-13y\) which are like terms because they share the same variable 'y' to the first power.

This means they can be combined by adding or subtracting the coefficients, which are the numbers in front of the variables. Simplifying like terms reduces the complexity of the expression, making it easier to manipulate. Here, combining \(2y - 13y\) effectively results in \(-11y\). Recognizing and simplifying like terms is crucial as it sets the stage for the next steps in solving equations, such as isolating variables.

Isolating the variable is a key part of solving equations, as it allows you to express the unknown explicitly in terms of known quantities. After simplifying the equation, the next step is to rearrange it so the variable is alone on one side. This often involves performing inverse operations.

In the given example, after combining like terms into \(-11y\), you need to isolate 'y'. You do this by dividing both sides of the equation by \(-11\).

• This step effectively "undoes" the multiplication of 'y' by \(-11\).
• Division is the inverse operation of multiplication.

Thus, you find that \(y = \frac{x}{-11}\). Mastering the skill of isolating variables is essential, as it enables you to solve for unknowns efficiently and accurately.