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When simplifying algebraic expressions, the order of operations is crucial. It determines which operations to perform first. An easy way to remember this is with the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the given problem, we start by removing parentheses. Although no complex operations such as multiplication or division are present, it is important to handle the subtraction and parentheses correctly. This ensures that the expression is simplified in the correct order. As seen in Step 1 of the solution, removing the parentheses allowed us to focus on simplifying the terms accurately without changing intended values.

Like terms are terms in an algebraic expression that have the same variables raised to the same power. They can be combined through addition or subtraction.
In our example, the expression is simplified by first identifying like terms. We look at the variable terms and constant terms separately. Variable terms like \(2x\) and \(-x\) are considered like terms because they both involve the same variable, \(x\). When combined, they simplify to \(x\). This step is crucial for reducing complexity in algebraic expressions.
Next, focus is given to the constant terms: \(-1\), \(-1\), and \(-2\). These do not have variables, so they too can be combined as like terms. Combining them results in the term \(-4\). Identifying and combining like terms help streamline the process of simplifying expressions.

Constants in algebra are numbers without attached variables. In our problem, constants are simply added or subtracted.
Since constants do not change, they act as a balancing element in an expression. In Step 2 of our solution, the constant terms\(-1\), \(-1\), and \(-2\) are added together. Their sum, \(-4\), is the constant part of the simplified expression.
While working with algebraic expressions, always set apart terms with constants so they can be factored into the final solution. By understanding constants, students can effectively simplify expressions and solve equations.