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How do you solve #10/(3x)-8=2/x# and find any extraneous solutions?

Answer 1

#x=1/6#

#10/(3x)-8=2/x# Multiply both sides by #x# #(10x)/(3x)-8x=2# #(10 cancelx)/(3 cancelx)-8x=2# Multiply both sides by #3# #(10xx3)/3-((8x)xx3)=2xx3# #(10xxcancel3)/cancel3-24x=6# #10-24x=6# #-24x=6-10=-4# #x=(-4)/(-24)=1/6#

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Answer 2

Kennedy Adams

To solve the equation 10/(3x) - 8 = 2/x and find any extraneous solutions, we can follow these steps:

Multiply both sides of the equation by the least common denominator (LCD), which is 3x. This eliminates the denominators.

10 - 24x = 6

Move all the terms involving x to one side of the equation and simplify.

-24x = 6 - 10

-24x = -4

Divide both sides of the equation by -24 to isolate x.

x = -4 / -24

Simplify the right side of the equation.

x = 1/6

To check for extraneous solutions, substitute the found value of x back into the original equation.

10/(3 * (1/6)) - 8 = 2/(1/6)

10/(1/2) - 8 = 12

20 - 8 = 12

12 = 12

Since the equation is true, there are no extraneous solutions. Therefore, the solution to the equation is x = 1/6.

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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.