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Chapter 2: Q56. (page 95)

Determine whether the following statement is sometimes, always, or never true. Explain your reasoning.

The sum of three consecutive odd integers equals an even integer.

Short Answer

Expert verified

The statement is never true.

Step by step solution

01

Step 1. Sum of two odd integers.

The sum of two odd numbers will always be an even number.

For example, Sum of 3 and 5 is 8.

02

Step 2. Sum of three odd integers.

If three odd integers are added together, the sum is always odd because the first two odd numbers will always sum to an even number, and the sum of this even number and the third odd number will always be odd.

03

Step 3. Few examples.

3+5+7=157+9+11=27

Hence, the statement is never true.

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Most popular questions from this chapter

GEOMETRY Two rectangular walls each with a length of 12 feet and a width of 23 feet need to be painted. It costs \(0.08 per square foot for paint. How much will it cost to paint the walls?

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Translate the following sentence into an equation:

“Two times z is equal to two times the sum of v and x”.

Compare and contrast solving equations with variables on both sides of the equation to solving one-step or multi-step equations with a variable on one side of the equation.

Translate the following sentence into an equation:

“Four times the sum of 14 and c is a squared”.

Which equation represents the second step of the solution process?

Step 1: 42x+7−6=3x

Step 2: _________________

Step 3: 5x+28−6=0

Step 4: 5x=−22

Step 5: x=−4.4

  1. 42x−6+7=3x
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  3. 8x+7−6=3x
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