Find 3 consecutive odd integers such that 1 less than 3 times the larger is equal to the sum of twice the first and twice the second number. Please explain why and with steps.

7, 9, 11

Step-by-step explanation:

If x is the smallest of the integers, then x+2 is the next consecutive odd integer, and x+4 is the largest odd integer.

1 less than 3 times the largest is equal to the sum of twice the first and twice the second.

3(x+4) − 1 = 2x + 2(x+2)

3x + 12 − 1  = 2x + 2x + 4

3x + 11 = 4x + 4

7 = x

The integers are 7, 9, and 11.

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Step-by-step explanation: