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Algebra is a powerful branch of mathematics that enables us to solve equations and understand relationships. In algebra, we often use variables like \(c\) to represent unknown values. These variables are used in equations to express mathematical ideas. An equation is essentially a balance scale, where both sides are equal. To solve an algebraic equation like \(8 - 2c = 2c\), our goal is to find the value of the variable that makes this statement true. We manipulate the equation using mathematical operations to isolate the variable. This process often involves moving terms from one side of the equation to the other, while maintaining the balance. It's important to apply the same operation on both sides when doing this adjusting, to keep the equation balanced.

After finding a solution to an equation, it's crucial to verify your result to ensure accuracy. Verification is the process of substituting the solution back into the original equation. This step confirms whether both sides of the equation remain equal. For instance, once we calculate \(c = 2\) in the equation \(8 - 2c = 2c\), we plug it back in: \(8 - 2(2) = 2(2)\).

This becomes \(8 - 4 = 4\) on both sides, confirming the correctness of our solution. Verification acts as a confirmation step, assuring us that no mistakes were made during the solving process. If the left side equals the right side after substitution, the solution is correct. If they don't match, it's a signal to go back and review the steps.

A key technique in solving algebraic equations is combining like terms. Like terms are terms that have the same variable raised to the same power. For example, \(-2c\) and \(2c\) are like terms because they both involve the variable \(c\). Combining these entails adding or subtracting the coefficients, the numbers in front of the variables, to simplify the equation. In the equation \(8 - 2c = 2c\), we add \(2c\) to both sides to combine the terms

• From \(-2c + 2c\) on the left, we get 0.
• Adding \(2c\) to the right results in \(4c\).

This simplification helps in isolating the variable, making the equation easier to solve. By mastering the art of combining like terms, you can efficiently simplify and solve complex algebraic expressions.