Question

four times the sum of the three consecutive even intergers is 240 more than six times the smallest integer.​

Answer 1

Answer is x = 36

Three even integers are
x = 36
x + 2 = 38
x + 4 = 40

Step by step

We know even integers = x, x + 2, x + 4

Our equation is

4(x + x + 2 + x + 4) = 6x + 240
Combine like terms in parentheses

4 (3x + 6) = 6x + 240
Multiply

12x + 24 = 6x + 240
Subtract 6x from both sides to combine variables

12x - 6x + 24 = 6x - 6x + 240
Simplify

6x + 24 = 240
Subtract 24 from both sides to combine constants

6x + 24 - 24 = 240 - 24
Simplify

6x = 216
Divide both sides by 6 to solve

6/6 x = 216/6

x = 36
x + 2 = 38
x + 4 = 40

Check your work using the original equation

4(x + x + 2 + x + 4) = 6x + 240

4 (36 + 36 + 2 + 36 + 4) = 6(36) + 240
Combine like terms inside parentheses

4(114) = 6(36) + 240
Multiply

456 = 456

They equal so solution is correct

Answer 2

Explanation:

Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".

Now we can set up the equation for the problem:

4 * (x + (x + 2) + (x + 4)) = 240 + 6x

Expanding the parentheses on the left side:

4 * (3x + 6) = 240 + 6x

Simplifying the left side:

12x + 24 = 240 + 6x

Subtracting 6x from both sides:

6x + 24 = 240

Subtracting 24 from both sides:

6x = 216

Dividing both sides by 6:

x = 36

So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.