Which expression is equivalent to $3 m+1-m$?
Answer (1)
Simplify the expression 3 m + 1 − m by combining like terms, resulting in 2 m + 1 . Compare the simplified expression with the given options to find the equivalent expression. The equivalent expression is 2 + m − 1 + m , which simplifies to 2 m + 1 . The final answer is 2 + m − 1 + m .
Explanation
Understanding the Problem We are asked to find the expression that is equivalent to 3 m + 1 − m . To do this, we need to simplify the given expression and then compare it to the provided options.
Simplifying the Expression First, let's simplify the expression 3 m + 1 − m by combining like terms. We have two terms with m : 3 m and − m . Combining these gives us 3 m − m = 2 m . So the expression simplifies to 2 m + 1 .
Comparing with Options Now, let's examine the given options and see which one is equivalent to 2 m + 1 :
Option 1: 2 + m − 1 + m . Combining like terms, we get m + m + 2 − 1 = 2 m + 1 . This is equivalent to our simplified expression.
Option 2: 1 + m . This is not equivalent to 2 m + 1 .
Option 3: 3 m − 1 . This is not equivalent to 2 m + 1 .
Option 4: 3 m . This is not equivalent to 2 m + 1 .
Finding the Equivalent Expression Therefore, the expression equivalent to 3 m + 1 − m is 2 + m − 1 + m .
Final Answer The equivalent expression is 2 m + 1 .
Examples
In retail, if a store marks up an item by 3 m dollars, then offers a discount of m dollars, and adds a fixed surcharge of $1 dollar, the final price increase is represented by the expression 3 m + 1 − m . Simplifying this to 2 m + 1 helps the store quickly calculate the net price change. For example, if m = 5 , the price increase is 2 ( 5 ) + 1 = 11 dollars.
