The sum of three consecutive even integers is 72 72 . Find the integers

Here we know that the sum of three consecutive even integers is 72, and we want to find the value of each of these integers. So to better understand what's going on here, let's draw a number line. And we'll put on some values like eight, nine, ten, eleven, and 12. So an example of three consecutive even integers would be eight, ten, and 12. So let's pretend that our first integer here is eight, so we'll call that integer x. We know that the difference between even integers is always two. So if our first integer is x, then our second integer is x plus two, and our third integer is x plus two plus an additional two, or x plus four. So we can build our equation by stating that x plus x plus two plus x plus four is equal to 72. Now we can solve for x. So combining our x values, we get three x plus two plus four is six. That's all equal to 72. Subtracting six from both sides, we have three x is equal to 66. And then dividing both sides by three, we get x is equal to 22. So if x is equal to 22, then our second integer is 22 plus two, and our third integer is 22 plus four. So we can state our answer as 22, 24, and 26.

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Multiple Choice

The sum of three consecutive even integers is $72$ . Find the integers

$22,24,26$

$20,22,30$

$23,24,25$

$18,24,30$

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Let the three consecutive even integers be represented as $x$, $x + 2$, and $x + 4$, where $x$ is the smallest even integer.

Write an equation expressing the sum of these three integers equal to 72: $x + (x + 2) + (x + 4) = 72$.

Combine like terms on the left side of the equation: \$3x + 6 = 72$.

Isolate the variable term by subtracting 6 from both sides: \$3x = 72 - 6$.

Solve for $x$ by dividing both sides by 3: $x = \frac{72 - 6}{3}$. Then find the three integers by substituting $x$ back into $x$, $x + 2$, and $x + 4$.

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The sum of three consecutive even integers is $72$ . Find the integers