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The "arithmetic mean" is the 'average'. The average of 2 numbers is 1/2 of their sum.

The numbers are (x-8) and (2x+1). We're told that half of their sum is 'x'.

1/2 [ (x-8) + (2x+1) ] = x

Fine! We are not intimidated.

Multiply each side by 2 ==> (x-8) + (2x+1) = 2x

Eliminate parentheses ==> x-8 + 2x+1 = 2x

Group the like-terms on the left side ==> x + 2x - 8 + 1 = 2x

Combine like-terms ==> 3x -7 = 2x

Add 7 to each side ==> 3x = 2x + 7

Subtract 2x from each side ==> x = 7

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15y ago

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