Answer:
The first integer is [tex]-2[/tex].
The second integer is [tex]-1[/tex].
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 [tex]x[/tex].
Therefore, the second integer is equal to [tex]x+1[/tex] 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,
[tex]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[/tex]
Substitute and Solve:
Now, we have, [tex]x=-2[/tex].
Substitute -2 for [tex]x[/tex] and solve for first and second integers. This gives,
The first integer value = [tex]x=-2[/tex]
The second integer value = [tex]1+x=1+(-2)=1-2=-1[/tex]
Therefore, the first integer is [tex]-2[/tex] and the second integer is [tex]-1[/tex].
