Students were asked to write an algebraic expression for the sum of three consecutive natural numbers x + (x + 1) + (x + 2) = 3x + 3. Another wrote (x - 1) + x + (x + 1) = 3x. Explain who is correct and why.
To determine who is correct, let's simplify each expression and compare the results.
The first expression, x + (x + 1) + (x + 2), represents the sum of three consecutive natural numbers.
Simplifying this expression:
x + (x + 1) + (x + 2) = 3x + 3
The second expression, (x - 1) + x + (x + 1), also represents the sum of three consecutive natural numbers.
Simplifying this expression:
(x - 1) + x + (x + 1) = 3x
By evaluating both expressions, we see that they are indeed equal. Both expressions simplify to 3x + 3, which shows that both students are correct.
In general, the sum of three consecutive natural numbers can be represented as 3x + 3, where x is the first of the three consecutive numbers. Both expressions are simply different ways of writing the same sum.