To determine the total time Hazel spends commuting to and from work each day, we need to add the expressions for the time to work and the time from work.
Given:
- Time to work: [tex]\( x + 6y \)[/tex]
- Time from work: [tex]\( 3x - 10y \)[/tex]
Step-by-Step Solution:
1. Write down the expressions for time to work and time from work:
- Time to work: [tex]\( x + 6y \)[/tex]
- Time from work: [tex]\( 3x - 10y \)[/tex]
2. Add the two expressions to find the total commuting time:
[tex]\[
\text{Total commuting time} = (x + 6y) + (3x - 10y)
\][/tex]
3. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( x + 3x = 4x \)[/tex]
- Combine the [tex]\( y \)[/tex] terms: [tex]\( 6y - 10y = -4y \)[/tex]
4. Write the simplified expression:
[tex]\[
\text{Total commuting time} = 4x - 4y
\][/tex]
Thus, the expression that represents the total time Hazel spends commuting to and from work each day is [tex]\( 4x - 4y \)[/tex].
Therefore, the correct choice is:
[tex]\[
\boxed{4x - 4y}
\][/tex]
