Expressing and Simplifying the Sum of Consecutive Even Integers

Q1. Write the sum of four consecutive even integers as an algebraic expression, if the first integer is x. Then simplify.

Background

Topic: Translating verbal statements into algebraic expressions and simplifying.

This question tests your ability to represent a sequence of consecutive even integers algebraically, then combine and simplify the resulting expression.

Key Terms and Formulas

• Consecutive even integers: Numbers that differ by 2 (e.g., 2, 4, 6, 8).

• Algebraic expression: A mathematical phrase involving variables and operations.

For four consecutive even integers starting with $x$, the sequence is:

• $x$ (first integer)

• $x + 2$ (second integer)

• $x + 4$ (third integer)

• $x + 6$ (fourth integer)

Step-by-Step Guidance

1. Write the sum of the four consecutive even integers as an algebraic expression: $x + (x + 2) + (x + 4) + (x + 6)$.

2. Remove the parentheses to combine all terms: $x + x + 2 + x + 4 + x + 6$.

3. Group like terms (all the $x$ terms together and all the constants together).

4. Combine the $x$ terms and the constants to form a simplified expression.

Try solving on your own before revealing the answer!