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How do you solve #\frac { 6} { 7x } = \frac { 4} { 5x - 1}#?

Answer 1

Multiply the fractions on each side of the equation by the same factor, which is the product of the denominators (#7x(5x - 1)#), to clear the fractions and keep the equation balanced:

#(7x(5x - 1) * 6)/(7x) = (7x(5x - 1)*4)/(5x - 1)#

#(cancel(7x)(5x - 1) * 6)/(cancel(7x)) = (7xcancel((5x - 1))*4)/cancel((5x - 1))#

#(5x -1)*6 = 7x*4#

We can now solve for #x# using the necessary mathematics while keeping the equation balanced:

#30x - 6 = 28x#

#30x - 28x - 6 + 6 = 28x - 28x + 6#

#2x = 6#

#(2x)/2 = 6/2#

#x = 3#

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Answer 2

Abigail Allen

To solve the equation (\frac{6}{7x} = \frac{4}{5x - 1}), we can cross-multiply to eliminate the fractions. This gives us (6(5x - 1) = 4(7x)). Expanding both sides of the equation, we get (30x - 6 = 28x). Next, we can isolate the variable by subtracting 28x from both sides, resulting in (2x - 6 = 0). Adding 6 to both sides gives (2x = 6), and finally, dividing both sides by 2 yields (x = 3). Therefore, the solution to the equation is (x = 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.