Question

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Answer 1

The first integer is
`-2`.

The second integer is
`-1`.

Explanation:

The five-step method is GUESS method.

Given:

6 times the sum of 2 consecutive integers is 13 less than five times the larger integer.

Unknown:

Value of first and second integer.

Let the first integer be
`x`.

Therefore, the second integer is equal to
`x+1` which is also the larger integer.

Evaluate:

6 times the sum of first and second integers is 13 less than five times the larger integer. So,

`6(x+x+1)=5(x+1)-13\\6(2x+1)=5x-5+13\\12x+6=5x-8\\12x-5x=-8-6\\7x=-14\\x=-(14)/(7)=-2`

Substitute and Solve:

Now, we have,
`x=-2`.

Substitute -2 for
`x` and solve for first and second integers. This gives,

The first integer value =
`x=-2`

The second integer value =
`1+x=1+(-2)=1-2=-1`

Therefore, the first integer is
`-2` and the second integer is
`-1`.