Question

1. (x - 2)/ 4 - (3x + 5)/7 = - 3, x = ?

2. 1/(1 + 1/(1 - 1/x)) = 4, X = ?
A. --3/4
B. 3/7
C. 4/7
D. 3/4
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Answer 1

1. x = 10
2. B. 3/7

Explanation:

1. (x - 2)/ 4 - (3x + 5)/7 = - 3

7(x -2) -4(3x +5) = -84 . . . . . . . multiply by 28

7x -14 -12x -20 = -84 . . . . . . . . eliminate parentheses

-5x -34 = -84 . . . . . . . . . . . . . . collect terms

-5x = -50 . . . . . . . . add 34

x = 10 . . . . . . . . . . . divide by -5

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2. 1/(1 + 1/(1 - 1/x)) = 4

1 = 4(1 +1/(1 -1/x)) . . . . multiply by the denominator

-3 = 4/(1 -1/x) . . . . . . . eliminate outer parentheses, subtract 4

-3(1 -1/x) = 4 . . . . . . . multiply by the denominator

-3 +3/x = 4 . . . . . . . . eliminate parentheses

3/x = 7 . . . . . . . . . . . add 3

x = 3/7 . . . . . . . . . . . multiply by x/7