Two times the least of three consecutive odd integers exceeds three times the greatest of 15. What are the integers?
I need an equation to solve and I have tried but without success can anyone help me?
Strange language; I suspect you meany "by" 15, so on that basis, we have
2x = 3(x+4)+15
-x = 27
x = -27
and the numbers are
-27 -25 -23
check:
-54 = -69+15
Let's assign variables to the three consecutive odd integers. Let's say the least is "n", the middle one is "n + 2", and the greatest is "n + 4".
Now let's set up the equation based on the given information: "Two times the least of three consecutive odd integers exceeds three times the greatest of 15."
2n = 3(n + 4)
We can simplify the equation:
2n = 3n + 12
Subtract 3n from both sides of the equation:
2n - 3n = 12
-n = 12
Multiply both sides by -1 to isolate the variable "n":
n = -12
Now substitute this value for "n" back into the equation to find the other two consecutive odd integers:
The least odd integer is n = -12. The middle one is n + 2 = -12 + 2 = -10. The greatest one is n + 4 = -12 + 4 = -8.
Therefore, the three odd integers are -12, -10, and -8.
To solve this problem, let's start by representing the three consecutive odd integers as x, x+2, and x+4.
We are given that two times the least of three consecutive odd integers exceeds three times the greatest of 15. In other words, 2x > 3(x+4).
Now, let's simplify the equation:
2x > 3x + 12.
To solve for x, we can subtract 3x from both sides of the inequality:
2x - 3x > 12.
Simplifying further:
-x > 12.
We can divide both sides by -1, but since we are dividing by a negative number, we need to reverse the inequality sign:
x < -12.
Therefore, the least odd integer is any number smaller than -12. We can choose a value for x, such as -13.
Therefore, the three consecutive odd integers are: -13, -11, and -9.