Question 1

If $$x is $$the first of four consecutive even integers, what is the algebraic expression for their sum, and what is its simplified form?

Accepted Answer

$$4x + 12$$

Question 2

Given four consecutive even integers starting with $$x$$, which of the following correctly represents the second integer?

Accepted Answer

$$x + 2$$

Question 3

Translate the phrase 'the sum of four consecutive even integers' into an algebraic expression if the first integer is $$x.$$

Accepted Answer

$$x + (x + 2) + (x + 4) + (x + 6)$$

Question 4

Which step is necessary to simplify the expression $$x + (x + 2) + (x + 4) + (x + 6)$$?

Accepted Answer

Remove parentheses and combine like terms

Question 5

If the sum of four consecutive even integers is $$52$$, what is the value of the first integer?

Accepted Answer

$$8$$

Question 6

Which of the following best describes the pattern for consecutive even integers?

Accepted Answer

Each integer is 2 more than the previous one

Question 7

If $$x is $$the first integer, what is the sum of the second and fourth consecutive even integers?

Accepted Answer

$$(x + 2) + (x + 6) = 2x + 8$$

Question 8

A real-world scenario: If four consecutive even numbers represent the ages of four siblings, and their total age is $$60$$, what is the age of the youngest sibling?

Accepted Answer

$$10$$

Question 9

Which of the following is NOT a correct way to write the sum of four consecutive even integers starting with $$x$$?

Accepted Answer

$$x + (x + 1) + (x + 2) + (x + 3)$$

Question 10

If the sum of four consecutive even integers is $$4x + 12$$, what is the sum if the first integer is $$5$$?

Accepted Answer

$$32$$

Question 11

Which of the following expressions represents the sum of four consecutive even integers if the first integer is $$x$$?

Accepted Answer

$$4x + 12$$

Question 12

If the sum of four consecutive even integers is $$4x + 12$$, and the sum is $$44$$, what is the value of $$x$$?

Accepted Answer

$$6$$

Question 13

Which step is required to solve for $$x if $$the sum of four consecutive even integers is $$4x + 12 = 52$$?

Accepted Answer

Subtract 12 from both sides, then divide by 4

Question 14

If the first integer is $$x$$, what is the third consecutive even integer?

Accepted Answer

$$x + 4$$

Question 15

Which of the following is a common mistake when writing the sum of four consecutive even integers?

Accepted Answer

Using $$x + (x + 1) + (x + 2) + (x + 3)$$ instead of $$x + (x + 2) + (x + 4) + (x + 6)$$

Expressing and Simplifying the Sum of Consecutive Even Integers

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