The biker needs to travel 65mi in four days and each day he needs to ride 1.5 the distance he did the day before.
In Part A you found that:
Day 1: 8 mi
Day 2: 1.5 (8mi)=12mi
Day 3: 1.5(12mi)=18mi
Day 4: 1.5(18mi)=27mi
This was just a recompilation of our previous results
Regarding part B
So, if x represents the distance traveled during the first day, once we add up each day we obtain the next expression:
Notice that the first term corresponds to the distance he bikes on the first day, the second term corresponds to the second day, and so on.
d represents the total distance during the 4 days
And remember, do not combine like terms!
This represents how much distance he will ride during the 4 days given the first-day distance
And, as you found in part A, if x=8, then 8.125(8)=65. So, our result is consistent.
Regarding Part C
Now, as our goal is to ride during 65mi, we only need to do d=65mi, giving us:
Regarding part D:
First, let's remember what 'like terms' mean:
An easy example of like terms is the next set: x, 2x, -7x
Notice that all of them share the term x, so they are 'like terms'
Going back to part C, we have that our final expression is:
As you can see, the left side of the equation contains terms that involve the x-factor, so all the terms on the left side are 'like terms' involving x
