Write the algebraic expression described. Simplify if possible.EXAMPLE 10If x is the first...

Write the algebraic expression described. Simplify if possible.

EXAMPLE 10

If x is the first of three consecutive integers, express the sum of the three integers in terms of x. Simplify if possible.

Solution

An example of three consecutive integers is

The second consecutive integer is always 1 more than the first, and the third consecutive integer is 2 more than the first. If x is the first of three consecutive integers, the three consecutive integers are

Their sum is

which simplifies to 3x + 3.

If x represents the first of two consecutive odd integers, express the sum of the two integers in terms of x.