The Iditarod, nicknamed “The Last Great Race on Earth,” is a dogsled race in Alaska. The 12- to 16-dog teams cover over 1150 miles in subzero weather. The record time for finishing the race is 218 hours (9 days, 2 hours). A dogsled race
Suppose a team takes 73 hours to
reach the first checkpoint of the Iditarod and 98 hours to reach the second.
How much time can be spent on the last leg of the race to beat the record time?
Let t represent the time for
the last leg of the race. Write an inequality.
If
this were an equation, we would subtract 171 from each side to solve for t. The same
procedure can be used with inequalities, as explained by the properties
below. This
problem will be solved in Example 2.
1.
Solve x + 14 ≥ 5. Check your solution.
Alternative Solutions:
Check: Substitute a number less than 9, the
number 9, and a number
greater than 9 into the inequality.
The solution is {all numbers greater than or equal to –9}.
A more concise way to express the
solution to an inequality is to use set-builder notation. The solution in Example 1 in set-builder
notation is {x│x ≥ –9}.
In Lesson 12–1, you learned that you
can show the solution to an inequality on a line graph. The solution, {x│x ≥ –9}, is shown below.
.PNG)
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2. Refer to the application at the beginning of the lesson. Solve 171 + t
< 218 to find the time needed to finish the last leg of the Iditarod and
beat the record.
Alternative Solutions:
The
solution can be written as {t│t < 47}. So any time less than 47 hours
will beat the record.
3. Solve 7y + 4 > 8y – 12. Graph the solution.
Alternative Solutions:
Since
16 > y is the same as y < 16, the solution is {y│y < 16}.
The
graph of the solution has a circle at 16, since 16 is not included. The arrow
points to the left.
You can also use inequalities to describe some geometry
concepts.
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