How do you solve and check for extraneous solutions in #4/v + 1/5 = 1#?

Answer 1

Isolate the term containing the variable; multiply to clear the denominators and divide by the constant to get #v=5# then plug the solution back into the original equation to verify.

Given #4/v+1/5=1#
Subtract #1/5# from both sides #color(white)("XXXX")##4/v = 4/5# (At this point it should be obvious that #v=5#, but continuing on...) Multiply both sides by #5v# #color(white)("XXXX")##4*5 = 4v# Divide by #5# #color(white)("XXXX")##v=5#
Verify that this is not an extraneous solution by substituting #color(red)(5)# for #v# in the original equation:
#color(white)("XXXX")##4/color(red)(5) + 1/5 = 1#
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Answer 2

To solve the equation 4/v + 1/5 = 1 and check for extraneous solutions, follow these steps:

  1. Multiply the entire equation by the least common denominator (LCD) of the fractions, which is 5v. This step eliminates the denominators.

5v * (4/v) + 5v * (1/5) = 5v * 1

  1. Simplify the equation by distributing and canceling out terms:

20 + v = 5v

  1. Move all terms involving v to one side of the equation:

v - 5v = -20

-4v = -20

  1. Divide both sides of the equation by -4 to isolate v:

v = -20 / -4

v = 5

  1. Substitute the found value of v back into the original equation to check for extraneous solutions:

4/5 + 1/5 = 1

This equation is true, so the solution v = 5 is valid and not extraneous.

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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.

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.

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.

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.

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