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When solving linear equations, combining like terms is an essential early step. Like terms are terms that have the same variable raised to the same power. For instance, in the expression on the left side of the equation \(6x - x\), both terms contain the variable \(x\).
To combine like terms, simply add or subtract their coefficients. Here, the coefficients are 6 and -1 (since \(-x\) is the same as \(-1x\)). Combining them, we get \(6x - x = 5x\). Combining like terms simplifies the equation and makes it easier to solve.
Remember, only like terms can be combined. Constants (numbers without variables) can be combined with other constants, and variable terms can be combined with other variable terms.

Isolating the variable is the core part of solving any linear equation. The goal is to get the variable on one side of the equation and the constants on the other.
In the given problem, after combining like terms, we have \(5x = -10\). To isolate \(x\), divide both sides of the equation by the coefficient of \(x\), which is 5. This will give us \(x = \frac{-10}{5}\). Simplifying this, we get \(x = -2\).
Isolating the variable often involves steps like adding, subtracting, multiplying, or dividing both sides of the equation by the same number. Make sure to perform the same operations on both sides to maintain the equality.
Keeping the equation balanced is crucial in isolating the variable.

Verifying the solution ensures that your answer is correct. After finding \(x = -2\) in the equation, we need to plug it back into the original equation to check if both sides are equal.
Substitute \(x = -2\) into the original equation: \(6(-2) - (-2) = 4 - 14\). Simplify both sides.
On the left side, \(6(-2)\) equals \(-12\), and subtracting \(-2\) is like adding 2, so \(-12 + 2 = -10\). On the right side, \(4 - 14 = -10\).
Since \(-10 = -10\), the solution is verified. Both sides of the equation are equal, confirming that \(x = -2\) is correct. This step is crucial for avoiding mistakes.

Basic algebra concepts are the foundation for solving equations. They involve understanding operations with numbers and variables. Key operations include addition, subtraction, multiplication, and division.
In the given problem, we used addition and subtraction to combine like terms and simplified the equation. We also used division to isolate the variable.
Remember, every operation you perform on one side of the equation must be performed on the other to keep it balanced. Additionally, simplifying expressions and verifying solutions are integral parts of basic algebra.
These fundamental skills are not only important for solving linear equations but also for more advanced math topics. Practicing basic algebra can greatly enhance your problem-solving abilities.