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Linear equations are equations of the form ax + b = c. These are called linear because they graph as straight lines. To solve them, we need to isolate the variable (usually x) on one side of the equation. Let's break it down into simple steps:1. **Identify the equation**: Start with the given equation. For example, in the exercise, the equation is 9x - 8x = 107.2. **Isolate the variable**: Move all terms involving the variable to one side and constants to the other. Since the example already has the variable on one side, it is simpler.3. **Solve for the variable**: Simplify and solve for the variable. After combining like terms, the equation reduces to x = 107.This method is standard for most linear equations, whether simple or complex.

Combining like terms is a technique used to simplify algebraic expressions. Like terms are terms that have the same variable raised to the same power. For instance, in the equation 9x - 8x,both terms are 'like' because they both have the variable x raised to the first power.Here’s how you combine like terms:1. **Identify like terms**: Look for terms that include the same variable and exponent. In our example, 9x and 8x are like terms.2. **Combine them**: Add or subtract the coefficients (numbers in front) of the like terms. So, 9x - 8x = (9 - 8)x = 1x = x.Combining like terms reduces the number of terms in the equation, making it simpler and easier to solve. This technique is a foundational skill in algebra.

An algebraic expression is a combination of numbers, variables (like x or y), and operators (such as +, -, *, /) that represent a value. Examples include 2x + 3and 9x - 8x.To understand and work with algebraic expressions, follow these steps:1. **Identify the components**: Recognize the variables, coefficients (numbers in front of variables), and constants (numbers without variables).2. **Simplify**: Use techniques like combining like terms and applying the distributive property to simplify the expression.3. **Translate and solve**: Sometimes, you'll need to translate words into algebraic expressions before solving. This was done in the given exercise, where 'the difference of 9x and 8x is 107' was translated to 9x - 8x = 107.Understanding the structure of algebraic expressions is crucial for solving equations and problem-solving in algebra.