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When faced with a mathematical equation, one of the fundamental steps is combining like terms. This involves grouping terms with similar variables or constants in order to simplify the equation.
For example, consider the expression \(7x - 9 - 9x - 4\). Here, the like terms are those involving \(x\), which are \(7x\) and \(-9x\). By combining them, you perform the operation \(7x - 9x\), resulting in \(-2x\).
Similarly, you should group the constant terms. In this case, \(-9\) and \(-4\) are constants. Adding them together simplifies to \(-13\).
By combining these like terms, the left side of the equation simplifies from \(7x - 9 - 9x - 4\) to \(-2x - 13\). This step makes it easier to isolate variables later on.

Isolating the variable is a crucial step when solving linear equations. The goal is to have the variable on one side of the equation to understand its value.
In our simplified equation \(-2x - 13 = -3x + 2\), you want to move all terms containing \(x\) to one side. To do this, you can add \(3x\) to both sides: \(-2x + 3x - 13 = 2\).
This transforms the equation into \(x - 13 = 2\). Notice how the \(x\) terms are now isolated on the left side.
Successfully isolating variable terms on one side of the equation is vital. It allows you to focus on finding the exact value of \(x\) next.

Simplifying equations is like tidying up a messy room to make sure everything is clear and easy to understand. It’s about getting the equation into its simplest form.
Once you have the variable isolated in an equation like \(x - 13 = 2\), you simply add 13 to both sides. This operation adjusts the equation to \(x = 2 + 13\).
Simplifying gives us \(x = 15\), the clean and clear solution for \(x\). The simpler an equation is, the easier it is to solve accurately. This practice ensures you solve the problem without extra confusion, avoiding mistakes and boosting confidence in math-solving skills.