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Answer :
Final answer:
To solve for x given the average of eight numbers is 5, we set up the equation (31 + 2x + 1) / 8 = 5 and found that x equals 4.
Explanation:
To find the value of x when the average of the numbers 5, 7, 2, 6, x, (x+1), 7, and 4 is 5, we'll use the formula for average:
- Add up all the numbers: 5 + 7 + 2 + 6 + x + (x + 1) + 7 + 4.
- Divide the total by the number of numbers. As there are 8 numbers in total, divide the sum by 8.
- Set up the equation: (31 + 2x + 1) / 8 = 5.
- Solve for x. Simplify the left side to get: (32 + 2x) / 8 = 5.
- Multiply both sides by 8 to get rid of the denominator: 32 + 2x = 40.
- Subtract 32 from both sides: 2x = 8.
- Divide both sides by 2: x = 4.
Therefore, the value of x is 4.
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