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Understanding how to combine like terms is a crucial skill in algebra. Combining like terms means grouping together terms that have the same variables raised to the same power.
For example, in the expression \[(x+1)+(x+2)+(x+3)\],
you'll notice there are multiple terms containing the variable \(x\). These \(x\) terms can be combined because they all share the same base variable with the same exponent, which in this case is 1 (though it's typically not written).
The numerical part of the terms, often called coefficients, is then summed up together.

• Here, \(x+x+x\)\ simplifies to \(3x\)\.
• The constant numbers without variables, which are \(1, 2,\) and \(3\), can similarly be added together to get \(6\)\.

Combining like terms not only simplifies an expression but also makes it easier to understand and work with. After combining like terms,
you end up with the simplified version: \(3x + 6\)\.

An algebraic expression is a mathematical phrase that includes numbers, variables, and operational symbols.
For instance, in the expression \((x+1)+(x+2)+(x+3)\),
\(x\) is a variable which represents a number that can change, and 1, 2, and 3 are constants which have fixed values.
The '+' signs between numbers and variables indicate that these numbers and variables are to be added together.
One of the main goals when working with algebraic expressions is to simplify them.

• This involves operations like combining like terms, performing arithmetic with coefficients and constants, and reducing the expression to its simplest form.

Simplifying expressions makes it easier to solve equations and perform other calculations. Each algebraic expression can typically be further simplified by understanding the roles of its various parts and how they relate to one another.

Basic algebra operations involve adding, subtracting, multiplying, and dividing terms in an expression.
In algebra, these operations are performed using similar rules as you would when working with numbers alone, but additional attention must be paid to the variables and constants involved.
In the exercise we are examining, addition is the primary operation.

• You grouped the like terms of \(x\)\ together to form \(3x\)\.
• The constants \(1+2+3\)\ were also added to produce \(6\)\.

Once these smaller operations were completed, the overall expression was greatly simplified. Recognizing where these basic operations can be applied and systematically carrying them out is what leads to a neat and simplified algebraic expression like this. Being comfortable with these basic operations is the foundation of solving more complex algebraic problems.