The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integers.

Answer:equation: (x-3) +(x-1) +(x+1) +(x+3) = -72values: -21, -19, -17, -15Step-by-step explanation:When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...   (x-3) +(x-1) +(x+1) +(x+3) = -72This simplifies to ...   4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.   x = -18 . . . . . . . . the middle number of the sequenceSo, the numbers are:-18-3 = -21-18-1 = -19-18+1 = -17-18+3 = -15_____A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...   (x) +(x +2) +(x +4) +(x +6) = -72and that simplifies to ...   4x +12 = -72 . . . . . collect terms   4x = -84 . . . . . . . . subtract 12   x = -21 . . . . . . . . . . divide by 4Now, the other three numbers are found by adding 2, 4, and 6 to this one.