Find the smaller of 2 consecutive integers, x, if the sum of the smaller and 6 times the larger is -29

-  The smaller integer is -5.

Explanation:-

Let the first consecutive integer be x and the second consecutive integer be x+1.

According to the given question:-

x+6(x+1)= -29

⇒x+6x+6= -29   [distributive law]

⇒x+6x= -29-6    [subtract 6 on the both sides]

⇒7x= -35      [combining like terms ]

⇒x= -5          [dividing 7 on both sides]

Thus the smaller integer =x= -5

larger integer =x+1= -5+1= -4