91Ó°ÊÓ

Combining like terms is a fundamental step in simplifying algebraic expressions. In order to solve linear equations, you first need to combine like terms on each side of the equation. Like terms are terms that have the same variable raised to the same power. For example, in the equation:
\(a + (a - 3) = (a + 2) - (a + 1)\), we start by simplifying each side of the equation.
On the left side:
\(a + (a - 3)\) can be combined as \(2a - 3\) (
since \(a\) and \(a\) are like terms).
On the right side:
\((a + 2) - (a + 1)\) simplifies to \(a + 2 - a - 1\). The \(a\) and \(-a\) terms cancel each other out,
leaving us with \(2 - 1 = 1\).
By combining like terms, we transform the original equation into a simpler equation:
\(2a - 3 = 1\). This makes it easier to solve for the variable.

Once we have combined like terms, the next step is to isolate the variable. The goal is to get the variable by itself on one side of the equation.
In the equation, \(2a - 3 = 1\), we want 'a' by itself. To do this:
1. Add 3 to both sides of the equation to remove the constant term on the left:
\(2a - 3 + 3 = 1 + 3\), which simplifies to \(2a = 4\).
2. Divide both sides by 2 to solve for \(a\):
\[a = \frac{4}{2} = 2\ \]. This process of isolating the variable helps us find the value of 'a' that satisfies the equation.

After finding the solution, it is crucial to check if it actually satisfies the original equation. This ensures our solution is correct.
Let's substitute \(a = 2\) back into the original equation:
\(a + (a - 3) = (a + 2) - (a + 1)\).
Replace 'a' with 2:
\(2 + (2 - 3) = (2 + 2) - (2 + 1)\). Simplify both sides:
\(2 + (-1) = 4 - 3\), which leads to \(1 = 1\).
Since both sides of the equation are equal, our solution \( a = 2\) is correct. Always check your solution to avoid any mistakes and to confirm that the value you found is indeed the correct one.