If you know how to solve word problems involving the sum of consecutive even integers, you should be able to easily solve word problems that involve the sum of consecutive odd integers. The key is to have a good grasp of what odd integers are and how consecutive odd integers can be represented.
Odd Integers
If you recall, an even integer is always 22 times a number. Thus, the general form of an even number is n=2kn=2k, where kk is an integer.
So what does it mean when we say that an integer is odd? Well, it means that it’s one less or one more than an even number. In other words, odd integers are one unit less or one unit more of an even number.
Therefore, the general form of an odd integer can be expressed as nn is n=2k-1n=2k−1 or n=2k+1n=2k+1, where kk is an integer.
Observe that if you’re given an even integer, that even integer is always in between two odd integers. For instance, the even integer 44 is between 33 and 55.
The solutions to the inequalities are x >1 and x < 6
<h3>How to solve the inequalities?</h3>
The inequality expression is given as:
-2x + 5 < 3x + 10
Collect the like terms in the above inequality
-2x - 3x < 10 - 5
Evaluate the like terms
-5x < 5
Divide by -5
x >1
Also, we have
5(x - 2) <3x + 2
Open the bracket
5x - 10 < 3x + 2
Evaluate the like terms
2x < 12
Divide by 2
x < 6
Hence, the solutions to the inequalities are x >1 and x < 6
Read more about inequalities at
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Answer: The commission is paid according to sales amounts that are likely to vary from month to month.
Step-by-step explanation: Instead of a salary that is paid in the same amount on a schedule, the commission may be very large one month and very small or zero at other times.
Financial planning usually includes monthly payments that and predictable expenses for food, transportation, utilities, etc. The person who earns a commission must remember to set aside some of the "extra" to cover these expenses. And be prepared to work more or harder at some times to make sales when they don't come easily.
We're given
which immediately tells us that
In other words, swapping the limits of the integral negates its value.
Also,
The integral we want to compute is
which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is
10 hours.
If you multiply 2 1/2 by 4, the product is 10.
