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How do you solve #\frac { 6} { z + 7} = \frac { 5} { z - 7}#?

Answer 1

Eva Abramson

#z=77#

#"one way is to "color(blue)"cross-multiply"#

#•color(white)(x)a/b=c/drArrad=bc#

#6(z-7)=5(z+7)larrcolor(blue)"distribute"#

#6z-42=5z+35#

#"subtract "5z" from both sides"#

#6z-5z-42=cancel(5z)cancel(-5z)+35#

#z=42=35#

#"add 42 to both sides"#

#z=35+42=77#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left "=6/(77+7)=6/84=1/14#

#"right "=5/(77-7)=5/70=1/14#

#"thus "x=77" is the solution"#

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Answer 2

Kennedy Adams

#z=77#

By cross multiplication we get #6(z-7)=5(z+7)# expanding #6z-42=5z+35# so #z=77#

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Answer 3

Avery Alexander

To solve the equation ( \frac{6}{z + 7} = \frac{5}{z - 7} ), we can cross-multiply to eliminate the fractions:

[ 6(z - 7) = 5(z + 7) ]

Next, distribute the numbers on both sides of the equation:

[ 6z - 42 = 5z + 35 ]

Combine like terms:

[ 6z - 5z = 35 + 42 ] [ z = 77 ]

Therefore, the solution to the equation is ( z = 77 ).

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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.