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Combining like terms is a method used to simplify algebraic expressions or equations. These 'like terms' have the same variable raised to the same power. In our example, we deal with the equation: \[a - \frac{3a}{2} = 1\]. The terms \(a\) and \(\frac{3a}{2}\) are like terms because they both contain the variable \(a\).
To combine them, we first find a common denominator. Here, the common denominator is 2. We rewrite \(a\) as \(\frac{2a}{2}\), making the equation read: \[\frac{2a}{2} - \frac{3a}{2} = 1\].
Next, we subtract the numerators: \(2a - 3a\), which simplifies to \(-a\). Thus, we get \[\frac{-a}{2} = 1\]. Combining like terms helps to simplify the equation, making it easier to solve.

Dealing with fractions in equations can be tricky. The goal is to simplify the equation to be free of fractions. In our example, we end up with a simplified form: \[\frac{-a}{2} = 1\].
To eliminate the fraction, we need to perform an operation that will clear it. In this case, we multiply both sides of the equation by -2. This step is crucial because it allows us to isolate the variable \(a\).
Multiplying both sides by -2: \[-2 \times \frac{-a}{2} = 1 \times -2\], results in: \[a = -2\].
This step helps to convert what may seem like a complicated fraction equation into a simpler form that can be more easily solved.

After solving an equation, it's important to check whether the solution is correct. This ensures that no computational errors have been made along the way. For our equation, we'll substitute \(a = -2\) back into the original equation: \[-2 - \frac{3(-2)}{2} = 1\].
First, work on the fraction: \[-2 - \frac{3(-2)}{2}\], simplifies to \[-2 - (-3)\]. Here, \(-\frac{3(-2)}{2} = 3\), so the expression now reads: \[-2 + 3\].
Finally, solving this gives: \[1 = 1\], confirming that our solution \(a = -2\) is indeed correct. Always make sure to substitute your solution back into the original equation when checking solutions. This process helps verify the accuracy of your solution and confirms you have followed the steps correctly.