Simplify x+2+x+2+x
The problem is asking you to perform algebraic simplification by combining like terms. Specifically, the terms given are all instances of 'x' or constant numbers that you need to add together to find a more compact or simplified expression, which in this case would be the sum of the x's and the constant numbers.
$x + 2 + x + 2 + x$
Answer
Solution:
Combining Like Terms
Step 1: Combine the $x$ terms. $x + x + x = 3x$.
Expression: $3x + 2 + 2$
Step 2: Add the constant terms together. $2 + 2 = 4$.
Expression: $3x + 4$
Step 3: The expression is now simplified.
Final Result: $3x + 4$
Knowledge Notes:
To simplify an algebraic expression, you follow the process of combining like terms. Like terms are terms that have the same variable raised to the same power. Here are the relevant knowledge points:
Combining Like Terms: This involves adding or subtracting coefficients of like terms. For example, $ax + bx = (a+b)x$.
Constants: These are numbers without variables and can be combined through addition or subtraction. For example, $c + d = c+d$.
Order of Operations: While simplifying, it's important to follow the order of operations, which typically isn't a concern with simple addition but becomes crucial with more complex expressions.
Coefficients: These are the numbers in front of the variables. When combining like terms, you only add the coefficients.
Variable Terms: These are parts of the expression that contain variables like $x$ or $y$. Only terms with the exact same variable and exponent can be combined.
Simplification: The process of reducing an expression to its simplest form by combining like terms and performing any operations possible.
In the given problem, we combined the $x$ terms and then the constant terms to simplify the expression. The use of LaTeX format for mathematical expressions ensures clarity and precision in presenting the solution.
