The expression [tex]$5 x -7$[/tex] represents the time it takes a commuter to travel in the morning to work. The expression [tex]$11 x -1$[/tex] represents the time it takes a commuter to travel in evening from work. What is the total travel time?
A. [tex]$16 x-6$[/tex]
B. [tex]$16 x+8$[/tex]
C. [tex]$16 x-8$[/tex]
D. [tex]$6 x-6$[/tex]
Answer (1)
Add the morning and evening travel time expressions: ( 5 x − 7 ) + ( 11 x − 1 ) .
Combine the x terms: 5 x + 11 x = 16 x .
Combine the constant terms: − 7 − 1 = − 8 .
The total travel time is 16 x − 8 .
Explanation
Understanding the Problem We are given two expressions representing the time it takes a commuter to travel to work in the morning and from work in the evening. We need to find the total travel time, which means we need to add the two expressions together.
Setting up the Addition The morning travel time is represented by the expression 5 x − 7 . The evening travel time is represented by the expression 11 x − 1 . To find the total travel time, we add these two expressions: ( 5 x − 7 ) + ( 11 x − 1 )
Combining Like Terms Now, we combine like terms. We add the terms with x together and the constant terms together: ( 5 x + 11 x ) + ( − 7 − 1 ) 16 x − 8
Final Answer The total travel time is represented by the expression 16 x − 8 .
Examples
Understanding how to combine expressions is useful in many real-life situations. For example, if you are tracking your expenses, you might have one expression for your fixed costs (like rent) and another for your variable costs (like groceries). Adding these expressions together gives you a total cost, helping you manage your budget effectively. Similarly, in physics, you might combine expressions for distance traveled at different speeds to find the total distance.
