The first step for solving this equation is to determine the defined range.
[tex] \frac{1}{4z} = - \frac{7}{8} + \frac{1}{8z} [/tex], z ≠ 0
Move the expression[tex] \frac{1}{8z} [/tex] to the left side of the equation and change its sign.
[tex] \frac{1}{4z} [/tex] - [tex] \frac{1}{8z} [/tex] = [tex]- \frac{7}{8} [/tex]
Now we need to write all numerators above the least common denominator of 8z. This will change the equation to the following:
[tex] \frac{1}{8z} [/tex] = [tex]- \frac{7}{8} [/tex]
Simplify the equation using cross multiplication.
8 = -56z
Switch the sides of the equation.
-56z = 8
Divide both sides of the equation by -56.
[tex]z = -\frac{1}{7} [/tex], z ≠ 0
Lastly,, check if the solution is in the defined range to get your final answer.
[tex]z = -\frac{1}{7} [/tex]
Let me know if you have any further questions.
:)
