2. find the smaller of 2 consecutive integers, x, if the sum of the smaller and the rest largeris-5.

-  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

The correct answer is -5.

Step-by-step explanation:

To start, we use x for the smaller integer. Then we can use that to write the equation as,

x + 6(x + 1) = -29

Now we solve for x.

x + 6x + 6 = -29

7x + 6 = -29

7x = -35

x = -5

Therefore the smaller of the two would be -5

You have defined x to be the smaller of two consecutive integers. Then the larger will be (x+1). The given relation is

... (x) + 3(x+1) = -5 . . . . the smaller plus 3 times the larger is -5

... 4x + 3 = -5 . . . . . . . .simplify

... 4x = -8 . . . . . . . . . . subtract 3

... x = -2 . . . . . . . . . . . divide by the coefficient of x

The smaller of the two integers is -2.