1. if the largest of three consecutive even integers is multiplied by 5, the product is 6 less than three times the sum of the first two integer. fin the integers.

Question

An attractive, mathematical and illustrative image showing three consecutive even numbers on blocks. The largest number block is visually multiplied by 5 inside a multiplication bubble. There is a minus 6 bubble nearby. Simultaneously, the first two number blocks are seen inside a sum bubble, that is then visually multiplied by 3. These two sides of the equation are shown on a scale to illustrate the balance. Please ensure the image has no text.

1. if the largest of three consecutive even integers is multiplied by 5, the product is 6 less than three times the sum of the first two integer. fin the integers.

Answer 1

(x+4)5 = 3(x + x+2)-6

Now just find x, the smallest number.

Answer 2

5(x+4)=3(2x+2)-6

5x+20=6x+6-6
5x+20=6x
5x-6x=-20
-x=-20
x=20

Answer 3

5(x+4)=3(2x+2)-6

5x+20=6x+6-6
5x+20=6x
5x-6x=-20
-x=-20
x=20

x+2=22
x+4=24

20,22,24

Answer 4

Why did the even integers go to the circus? Because they wanted to find their missing clown, "X"! Let's join them on their adventure:

Let's assume the first even integer is "X", the second one is "X + 2", and the third one is "X + 4".

According to the problem, the largest integer (X + 4) multiplied by 5 is 6 less than three times the sum of the first two integers (X + X + 2):

5(X + 4) = 3(X + X + 2) - 6

Now, let's solve this equation together and find those mysterious integers:

5X + 20 = 3(2X + 2) - 6

5X + 20 = 6X + 6 - 6

5X + 20 = 6X

20 = 6X - 5X

20 = X

So, the first even integer is 20.

The second integer: X + 2 = 20 + 2 = 22

And the third integer: X + 4 = 20 + 4 = 24

Therefore, the three consecutive even integers are 20, 22, and 24. Ta-da!

Answer 5

To solve this problem, let's assign variables to represent the consecutive even integers.

Let's say the first even integer is x, the second is (x + 2), and the third is (x + 4).

According to the problem, "the largest of three consecutive even integers is multiplied by 5." So, we can create the equation:

5 * (x + 4)

The problem also states, "the product is 6 less than three times the sum of the first two integers." We can represent this as:

3 * (x + (x + 2)) - 6

Now we can set up the equation:

5 * (x + 4) = 3 * (x + (x + 2)) - 6

Simplifying this equation will give us the value of x.

5x + 20 = 3x + 3x + 6 - 6

5x + 20 = 6x + 6

Now, let's solve for x:

5x - 6x = 6 - 20

-x = -14

x = 14

Now that we have the value of x, we can find the other two consecutive even integers:

The first even integer is 14.
The second even integer is (14 + 2) = 16.
The third even integer is (14 + 4) = 18.

Therefore, the three consecutive even integers are 14, 16, and 18.