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How do you solve #14/(x - 8) + 2 = 10/(x - 8)#?

Answer 1

Genesis Allen

#x=6#

Assuming #x ne 8#, we can convert the expression into

#\frac{14}{x-8} + \frac{2(x-8)}{x-8} = \frac{10}{x-8}#

And thus

#\frac{14+2(x-8)}{cancel(x-8)} = \frac{10}{cancel(x-8)}#

Expanding the first numerator, we have #14+2x-16 = 2x-2#

So, the equation becomes #2x-2 = 10#, and finally #2x=12 -> x=6#

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Answer 2

Eva Abramson

To solve the equation 14/(x - 8) + 2 = 10/(x - 8), you can start by multiplying both sides of the equation by (x - 8) to eliminate the denominators. This gives you 14 + 2(x - 8) = 10. Simplify the equation by distributing 2 to the terms inside the parentheses: 14 + 2x - 16 = 10. Combine like terms: 2x - 2 = 10 - 14. Simplify further: 2x - 2 = -4. Add 2 to both sides of the equation: 2x = -4 + 2. Simplify: 2x = -2. Finally, divide both sides of the equation by 2 to solve for x: x = -2/2. Therefore, x = -1.

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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.