Question

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

Answer 1

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