Problem 1
x = some unknown number
3x = three times a number
3x-7 = difference of three times a number and seven
2(3x-7) = two times the difference of three times a number and seven
2(3x-7) = x
The last equation is formed because the expression we built up is equal to the original number in question
<h3>Answer: 2(3x-7) = x</h3>
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Problem 2
Use the distribution rule to get
3(2x+4)-2x
3*2x+3*4-2x
6x+12-2x
From here, we combine like terms. That means we combine the 6x and -2x to get 4x
So 6x+12-2x simplifies to 4x+12 and not 16x
How did she get 16x? Possibly because she mistakenly thought she could add 4x to 12 to get 16x. This only works if the 12 had x attached to it.
In other words, this is valid: 4x+12x = 16x but this is not 4x+12 = 16x
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Problem 3
L = length = horizontal dimension = (d+15) ft
W = width = vertical dimension = (d-3) ft
P = perimeter of the rectangle = 108 ft
P = 2(L+W)
108 = 2(d+15+d-3)
108 = 2(2d+12)
108 = 4d+24
4d+24 = 108
4d = 108-24
4d = 84
d = 84/4
d = 21
The deep end is 21 feet long.
This means the overall horizontal length is d+15 = 21+15 = 36 feet and the the vertical width is d-3 = 21-3 = 18 feet
The overall dimensions of the rectangular pool are 36 ft by 18 ft
<h3>Answer: d = 21</h3>
