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How do you solve #7/(a-4)=14/6#?

Answer 1

Savannah Anderson

#a=7#

Simplify the fraction on the right side by dividing numerator/denominator by 2

#rArrcancel(14)^7/cancel(6)^3=7/3#

#rArr7/(a-4)=7/3#

Since the numerators are equal then the denominators must be equal.

#rArra-4=3#

add 4 to both sides.

#acancel(-4)cancel(+4)=3+4#

#rArra=7#

#color(blue)"As a check"#

Substitute this value into the left side and if equal to the right side then it is the solution.

#7/(7-4)=7/3=" right side"#

#rArra=7" is the solution"#

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Answer 2

Julia Adams

To solve the equation 7/(a-4) = 14/6, you can start by cross-multiplying. This means multiplying the numerator of the first fraction (7) by the denominator of the second fraction (6), and vice versa. This gives you 7 * 6 = 42 on the left side and (a-4) * 14 = 14a - 56 on the right side.

Now, you have the equation 42 = 14a - 56. To isolate the variable, you can add 56 to both sides of the equation, resulting in 42 + 56 = 14a. Simplifying this gives you 98 = 14a.

To solve for 'a', divide both sides of the equation by 14. This gives you 98/14 = a. Simplifying further, you get a = 7.

Therefore, the solution to the equation 7/(a-4) = 14/6 is a = 7.

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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.