The expression $4x+13$ represents the time it takes a commuter to travel in the morning to work. The expression $10x-2$ represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
A. $14x+15$
B. $14x+11$
C. $6x+11$
D. $6x+15$
Answer (2)
Add the morning and evening travel time expressions: ( 4 x + 13 ) + ( 10 x − 2 ) .
Combine the x terms: 4 x + 10 x = 14 x .
Combine the constant terms: 13 − 2 = 11 .
The total travel time is 14 x + 11 .
Explanation
Understanding the Problem We are given two expressions representing the morning and evening travel times. The morning travel time is 4 x + 13 , and the evening travel time is 10 x − 2 . We need to find the total travel time, which is the sum of these two expressions.
Adding the Expressions To find the total travel time, we add the two expressions: ( 4 x + 13 ) + ( 10 x − 2 ) Now, we combine like terms. We add the terms with x and the constant terms separately.
Combining Like Terms Combining the x terms: 4 x + 10 x = 14 x Combining the constant terms: 13 − 2 = 11 So, the total travel time is: 14 x + 11
Final Answer The total travel time is 14 x + 11 .
Examples
Understanding how to combine expressions like this is useful in many real-life situations. For example, if you're planning a road trip, you might use expressions to represent the distance you'll travel each day. If the distance on the first day is 5 x + 20 miles and the distance on the second day is 3 x + 10 miles, the total distance for the trip would be ( 5 x + 20 ) + ( 3 x + 10 ) = 8 x + 30 miles. Knowing how to simplify and combine these expressions helps you quickly calculate the total distance, time, or cost of your trip.
The total travel time for the commuter is represented by the expression 14 x + 11 . This is found by adding the morning and evening travel time expressions and combining like terms. Therefore, the correct answer is option B, 14 x + 11 .
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