three consecutive integers such that 3 times the sum of the first and second is one greater than 4 times the third.?

Remark

I take it you want the integers to this problem.

Givens

The smallest integer = x - 1

The middle integer = x

The largest integer = x + 1

Equation

3 (x - 1 + x) = 4 (x + 1) + 1 Remove the brackets on both sides.

3 (2x - 1) = 4x + 4 + 1

6x - 3 = 4x + 5 Subtract 5 from both sides.

-3 - 5 + 6x = 4x

- 8 + 6x = 4x Subtract 6x from both sides

- 8 = 4x - 6x

- 8 = - 2x Divide by - 2

-8/-2 = x

x = 4

Check

smallest integer = 3

middle integer = 4

largest integer = 5

3 (3 + 4) = 4 (5) + 1

3 (7) = 4 (5) + 1

21 = 20 + 1

21 = 21 and it checks.

Answer

the smallest number is 3

the middle number is 4

The largest number = 5