Answer: 0 ≤ x < 74
This is the same as x < 74 when x is nonnegative.
In either case, x is an integer.
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Explanation.
x = number of crossings in a 3 month period
The three-month pass charges a start fee of $18. Then tacks on $0.50 per crossing. Doing x number of these crossings means we add 0.50x dollars onto the $18 initially.
The total cost of the three-month pass is 18+0.50x dollars.
The six-month pass costs $55 with no extra fees. You can cross as many times as you want, and only pay $55 total for the entire three month period.
To find out when the three-month pass is better than the six-month pass, we will form this inequality: 18+0.5x < 55. The stuff on the left is the three-month pass, and the right hand side is the six-month pass.
Let's solve for x.
18+0.5x < 55
0.5x < 55-18
0.5x < 37
x < 37/0.5
x < 74
If you make fewer than 74 crossings, then the three-month pass is the cheaper option.
For example, if you do x = 60 crossings then,
18+0.5x = 18+0.5*60 = 18+30 = 48 dollars is the total, which beats the $55 from the other plan.
On the other hand, if you do x = 90 crossings, then,
18+0.5x = 18+0.5*90 = 18+45= 63 dollars is the total, which is now more expensive compared to the $55.
Because x is a nonnegative number, we can expand x < 74 into 0 ≤ x < 74 to be more clear what values x can take on.
Both x < 74 and 0 ≤ x < 74 are valid answers. If you go with the first one, then be sure to state that x cannot be negative. In either case, x is an integer. We cannot have something like x = 2.189 crossings.