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Answer :
To solve the problem of finding the equation that represents the sum of three consecutive even integers equaling 66, let’s break it down step by step:
1. Identify the Variables:
- Let [tex]\( x \)[/tex] represent the first even integer.
2. Express the Consecutive Integers:
- Since the integers are consecutive even numbers, the next numbers would be:
- The second integer: [tex]\( x + 2 \)[/tex]
- The third integer: [tex]\( x + 4 \)[/tex]
3. Set Up the Equation:
- According to the problem, the sum of these three consecutive even integers is 66. Therefore, you can write the equation as:
[tex]\[
x + (x + 2) + (x + 4) = 66
\][/tex]
4. Verify the Equation:
- Combine like terms:
[tex]\[
x + x + x + 2 + 4 = 66
\][/tex]
[tex]\[
3x + 6 = 66
\][/tex]
- This confirms that the equation [tex]\( x + (x + 2) + (x + 4) = 66 \)[/tex] accurately represents the scenario where the sum of three consecutive even integers is 66.
Therefore, the correct equation that represents the scenario is [tex]\( x + (x + 2) + (x + 4) = 66 \)[/tex].
1. Identify the Variables:
- Let [tex]\( x \)[/tex] represent the first even integer.
2. Express the Consecutive Integers:
- Since the integers are consecutive even numbers, the next numbers would be:
- The second integer: [tex]\( x + 2 \)[/tex]
- The third integer: [tex]\( x + 4 \)[/tex]
3. Set Up the Equation:
- According to the problem, the sum of these three consecutive even integers is 66. Therefore, you can write the equation as:
[tex]\[
x + (x + 2) + (x + 4) = 66
\][/tex]
4. Verify the Equation:
- Combine like terms:
[tex]\[
x + x + x + 2 + 4 = 66
\][/tex]
[tex]\[
3x + 6 = 66
\][/tex]
- This confirms that the equation [tex]\( x + (x + 2) + (x + 4) = 66 \)[/tex] accurately represents the scenario where the sum of three consecutive even integers is 66.
Therefore, the correct equation that represents the scenario is [tex]\( x + (x + 2) + (x + 4) = 66 \)[/tex].
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