Four consecutive integers

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Question from Mickey, a student:

Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer.
I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3

Hi Mickey,

If x is an integer then the expression you wrote

x + x + 1 + x + 2 + x + 3

is the sum of four consecutive integers. The four consecutive integers are

x, x + 1, x + 2, and x + 3.

The first three are

x, x + 1 and x + 2

and hence the sum of the first three is

x + x + 1 + x + 2.

This sum is 20 more than the fourth integer x + 3. Write an equation that says "x + x + 1 + x + 2 is 20 more than x + 3". Solve for x.

Penny

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