Question

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Answer 1

Answer:

The first integer is $-2$.

The second integer is $-1$.

Step-by-step 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,

$6(x+x+1)=5(x+1)-13\\6(2x+1)=5x-5+13\\12x+6=5x-8\\12x-5x=-8-6\\7x=-14\\x=-\frac{14}{7}=-2$

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 $-1$.