For three consecutive odd integers, the sum of 3 times the first integer and 2 times the second integer is 7 less than 4 times the third integer. What are the three integers?
Separate your answers with commas. Ex: 1,2,3
Please show work thank you
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To solve this problem, let's represent the three consecutive odd integers as x, x + 2, and x + 4.
According to the problem, the sum of 3 times the first integer and 2 times the second integer is 7 less than 4 times the third integer. Mathematically, this can be expressed as:
3x + 2(x + 2) = 4(x + 4) - 7
Now, let's solve the equation step by step:
3x + 2x + 4 = 4x + 16 - 7
Combine like terms:
5x + 4 = 4x + 9
Subtract 4x from both sides:
5x - 4x + 4 = 9
Simplify:
x + 4 = 9
Subtract 4 from both sides:
x = 9 - 4
x = 5
Now that we have the value of x, we can substitute it back into the original expression to find the other two integers:
The three integers are: 5, 7, 9
So, the solution is 5, 7, 9.