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Writing Algebraic Expressions

Consider the three consecutive integers 5, 6, and 7. Note that each integer is 1 larger than the previous integer. To represent three unknown consecutive integers, we let

  x = the first integer,
x + 1 = the second integer,
and x + 2 = the third integer.

Consider the three consecutive odd integers7, 9, and 11. Note that each odd integer is 2 larger than the previous odd integer. To represent three unknown consecutive odd integers, we let

  x = the first integer,
x + 2 = the second integer,
and x + 4 = the third integer.

Note that consecutive even integers as well as consecutive odd integers differ by 2. So the same expressions are used in either case.

How would we represent two numbers that have a sum of 8? If one of the numbers is 2, the other is certainly 6, or 8 - 2. So if x is one of the numbers, then 8 - x is the other number. The expressions x and 8 - x have a sum of 8 for any value of x.

 

Example 1

Writing algebraic expressions

Write algebraic expressions to represent each verbal expression.

a) Two numbers that differ by 12.

b) Two consecutive even integers.

Solution

a) The expressions x and x + 12 differ by 12. Note that we could also use x and x - 12 for two numbers that differ by 12.

b) The expressions x and x + 2 represent two consecutive even integers.

 
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