Question

The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.

x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42

Answer 1

• A and C are correct choices

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The difference between two consecutive integers is 1.

Test it with the given choices

A) x + (x + 1) + (x + 2) = 42,

• Yes

B) x + (x + 2) + (x + 4) = 42

• No, the difference between the pairs is 2 not 1.

C) (x minus 1) + x + (x + 1) = 42

• Yes

D) (x minus 2) + x + (x + 2) = 42

• No, the difference between the pairs is 2 not 1.

E) x + 2 x + 3 x = 42

• No, here is the multiples of integers and the difference between the pairs is x not 1.

Answer 2

x + (x + 1) + (x + 2) = 42

(x minus 1) + x + (x + 1) = 42

Explanation:

Integer: A whole number that can be positive, negative, or zero.

Consecutive integer: Integers that follow each other in order.

Let x be an integer.

Consecutive integers of x are one more or one less than each other in order.

• x + (x + 1) + (x + 2) = 42

This equation represents 3 consecutive integers as each value is one more than the previous value.

• x + (x + 2) + (x + 4) = 42

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

• (x minus 1) + x + (x + 1) = 42

This equation represents 3 consecutive integers as each value is one more than the previous value.

• (x minus 2) + x + (x + 2) = 42

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

• x + 2 x + 3 x = 42

This equation does not represent 3 consecutive integers as each value is x more than the previous value.