Respuesta :

bcalle
First, to set up consecutive odd or even integers you have to add 2 to the previous integer.
Let x be the first integer,
(x + 2), (x + 4), and (x + 6)

Now set up the parameters they give:
3(x + x + 2) = x + 6 - 25
Solving:
Combine like terms and distribute on the left, combine like terms on the right.
3(2x + 2) = x - 19
6x + 6 = x - 19
Subtract x from both sides and subtract 6 from both sides.
5x = -25
Divide both sides by 5
x = -5
x + 2 = -5 + 2 = -3
x + 4 = -5 + 4 = -1
x + 6 = -5 + 6 = 1
Check:
3(-5 + -3) ?=? 1 - 25
-24 ?=? -24 CORRECT

The four consecutive odd integers are -5, -3, -1, 1.

What is an odd integer?

"These are the integers which cannot be completely divide by 2."

What is consecutive odd integers?

"These are odd integers that follow each other and they differ by 2."

For given example,

Let, x, x + 2, x + 4, x + 6 be four consecutive odd integers.

These integers are such that three times the sum of the first and second is 25 less than the fourth

⇒ 3 × ((x) + (x + 2)) = (x + 6) - 25

⇒ 3 × (2x + 2) = x + 6 - 25

⇒ 6x + 6 = x - 19

⇒ 6x + 6 - x = x - 19 -x

⇒ 6x +6 - 6 = -19 - 6

⇒ 5x = -25

⇒ x = -5

So, the first odd integer is x = -5

the second odd integer would be,

= x + 2

= -5 + 2

= -3

the third odd integer would be,

= x + 4

= -5 + 4

= -1

the fourth odd integer would be,

= x + 6

= -5 + 6

= 1

Hence, the four consecutive odd integers are -5, -3, -1, 1.

Learn more about consecutive odd integers here:

https://brainly.com/question/11950105

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