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If the mean of three values 3x, 2x+6 and 2x+1 is 7, then find x.
8
4
6
2
2
Since the mean is 7 and there are 3 values, their sum must be 21. Mentally sum the coefficients (3+2+2 = 7) and constants (6+1 = 7) to get 7x + 7 = 21, leading directly to 7x = 14.
Three values are 3x, 2x+6, and 2x+1. The mean of these values is 7.
Mean=Number┬аof┬аValuesтИСValuesтАЛ
Since the mean is 7 and there are 3 values, their sum must be 21. Mentally sum the coefficients (3+2+2 = 7) and constants (6+1 = 7) to get 7x + 7 = 21, leading directly to 7x = 14.
Many students miscalculate the sum of the terms or divide the total sum by the wrong number of observations.
Set up the equation
The mean of the three values is 7, so the sum of the values divided by 3 equals 7.
33x+(2x+6)+(2x+1)тАЛ=7
Simplify the expression
Combine the like terms in the numerator: 3x+2x+2x=7x and 6+1=7.
37x+7тАЛ=7
Solve for x
Multiply both sides by 3 to get 7x+7=21. Then, subtract 7 from both sides to get 7x=14, and divide by 7.
x=714тАЛ=2
D is correct because solving the equation 7x+7=21 results in x=2.
This concept of equating the mean to a sum is frequently used in Algebra to find missing variables in data sets and is foundational for topics like Weighted Averages.
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