At the heart of algebraic expressions lies the fundamental question: which expression is equivalent to 3m+1-m? Embark on an enlightening journey as we delve into the intricacies of this expression, uncovering its hidden simplicity through a systematic approach.
Unraveling the mysteries of variables and constants, we will illuminate the order of operations and the transformative power of the distributive property. Like puzzle pieces falling into place, we will combine like terms, leading us to the final result—a testament to the elegance of mathematical simplification.
Equivalent Expression
The expression “3m+1-m” can be simplified to an equivalent expression by combining like terms.
First, we can group the terms with the variable m together:
- m
- m = 2m
Then, we can simplify the expression further by subtracting the constant term from the variable term:
m + 1 = 2m + 1
Therefore, the equivalent expression for “3m+1-m” is 2m + 1.
Variable and Constant Identification
In the expression “2m + 1”, the variable is m and the constant is 1.
A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.
Order of Operations
To evaluate the expression “2m + 1”, we need to follow the order of operations:
- Parentheses first
- Exponents (powers)
- Multiplication and division (from left to right)
- Addition and subtraction (from left to right)
In this case, there are no parentheses or exponents, so we can move directly to multiplication and division. There are no multiplication or division operations, so we can move on to addition and subtraction.
Therefore, we can evaluate the expression as follows:
m + 1 = 2(5) + 1 = 10 + 1 = 11
Distributive Property
The distributive property states that a(b + c) = ab + ac.
We can use the distributive property to simplify the expression “2m + 1” as follows:
m + 1 = 2(m + 1/2)
This shows that the distributive property can be used to break down an expression into simpler terms.
Combining Like Terms
Like terms are terms that have the same variable and exponent.
In the expression “2m + 1”, the like terms are 2m and 1.
We can combine like terms by adding their coefficients:
m + 1 = 2m + 1 = 3m
Final Result, Which expression is equivalent to 3m+1-m
The final result of the simplified expression is 3m.
This expression represents the sum of 2m and 1.
Essential Questionnaire: Which Expression Is Equivalent To 3m+1-m
What is the simplified form of “3m+1-m”?
The simplified form is “2m+1.”
How do you simplify “3m+1-m”?
Combine like terms by subtracting “m” from “3m” to get “2m.” The expression becomes “2m+1.”
What is the distributive property?
The distributive property states that a(b+c) = ab+ac. It allows us to multiply a term outside the parentheses by each term inside the parentheses.
