Find three consecutive integers such that the largest is 3 less than twice the smallest

The three consecutive integers are 5,6,7

Step-by-step explanation:

Let the three consecutive integers be represented as x, x+1, x+2

As per the requirement, largest integer is 3 less than twice the smallest.

=> x + 2 = 2x - 3

=> 2x - x = 2+3

=> x = 5

So the three integers are 5,6,7

Verification:

Largest integer = 7

Smallest integer = 5

2 * smallest integer - 3 = 2 * 5 - 3 = 7

Largest integer is also 7.

So the required condition in the question is satisfied by these three integers.