If x ≠ 0, what is the solution to the following equation? (1 - x)/x + 2 = 7/x

Could also write this as

 $$\frac{1}{x}-1+2=\frac{7}{x}$$

or

$$1=\frac{6}{x}$$

Multiply both sides by x to get x = 6

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If x ≠ 0, what is the solution to the following equation? (1 - x)/x + 2 = 7/x

Getting a common denominator on the left, we have

(1 - x)/x + 2x/x  = 7/x    subtract 2x/x from both sides

(1 -x)/ x  = 7/x - 2x/x

(1-x )/x  = (7 - 2x) /x     cross-multiply

x(1 - x)  = x(7 - 2x)    simplify

x - x^2  = 7x - 2 x^2  rearrange

x^2 - 6x = 0  factor

x(x -6) = 0     set both factors = 0...so x = 0 or  x = 6

And since x can't = 0,   then x = 6 

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