help with equations

Let x be the largest integer.

First find the sum of the integers:

$x+(x-1)+(x-2)+(x-3)+(x-4)+(x-5)+(x-6)$

Simplify:

$7x-21$

Now, since the sum or 7x - 21 is 21 times the largest of the integers or x, we can solve for x:

$7x-21=21x$

$-21=14x$

$-1.5=x$

Now we know the largest of the integers is -1.5.

To find the smallest integer, all we need to do is subtract 6 from -1.5:

$-1.5-6=-7.5$

The smallest integer Pearl wrote down was -7.5.

The smallest integer that Pearl wrote down is 15.

Step-by-step explanation:

7 consecutive integers. They are:

a

a+1

a+2

a+3

a+4

a+5

a+6

Sum of the integers:

a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 = 7a + 21

6 times the largest of the seven integers.

The largest is a + 6. So

7a + 21 = 6(a + 6)

7a + 21 = 6a + 36

7a - 6a = 36 - 21

a = 15

The smallest integer that Pearl wrote down is 15.