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When simplifying algebraic expressions, one of the key steps involves combining like terms. Like terms are terms in an expression that contain the same variables raised to the same power. For example, in the expression \(3x - 4x\), both terms are "like" because they share the variable \(x\). To combine them, simply add or subtract the coefficients: \(3 - 4 = -1\). So, \(3x - 4x\) simplifies to \(-x\).

• Identify terms with the same variable and power.
• Add or subtract the coefficients.
• Keep the common variable part unchanged.

This step is critical as it helps reduce the complexity of the expression by minimizing the number of separate terms.

Simplifying expressions makes them easier to work with by reducing the number of terms and operations. The process generally involves a series of steps starting with removing parentheses or any distributive operations, combining like terms, and then reducing constants. Let's consider the original expression from the exercise: \(3x - 7 + 1 - 2x \times 2\).
First, simplify any operations within the expression. Here, \(-2x \times 2 = -4x\). Next, we combine like terms: \(3x\) and \(-4x\) become \(-x\). Finally, combine the constant terms \(-7 + 1 = -6\).
The expression is now in its simplest form: \(-x - 6\). Simplification achieves a more concise formula, making computations and further algebraic processes more straightforward.

In algebraic expressions, constants are numbers on their own, without any attached variables. These play an essential role in the simplification process. In our working example, the constants are \(-7\) and \(+1\). Unlike terms with variables, constants can be combined just like regular numbers in arithmetic.
Here are key points to handle algebraic constants:

• Look for standalone numbers in the expression.
• Add or subtract them just as you would with simple numbers.
• Ensure numerical accuracy to avoid errors in the final outcome.

In our exercise, adding \(-7\) and \(+1\) results in \(-6\). This step reduces the expression to its most concise form and ensures clarity, especially when performing further algebraic operations.