Answer:
-3
Step-by-step explanation:
x + (x+1) +(x+2)+(x+3)+(x+4)+(x+5)+(x+6) = 0
7x + 21 = 0
x = -3
The value of the smallest integer is [tex]-3[/tex].
Given:
The sum of seven consecutive integers is zero.
To find:
The value of the smallest integer.
Explanation:
Let [tex]x[/tex] be the smallest integer, then the seven consecutive integers are [tex]x,x+1,x+2,x+3,x+4,x+5,x+6[/tex].
It is given that the sum of seven consecutive integers is zero.
[tex]x+x+1+x+2+x+3+x+4+x+5+x+6=0[/tex]
[tex]7x+21=0[/tex]
[tex]7x=-21[/tex]
Divide both sides by [tex]7[/tex].
[tex]\dfrac{7x}{7}=\dfrac{-21}{7}[/tex]
[tex]x=-3[/tex]
Therefore, the value of the smallest integer is [tex]-3[/tex].
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