Question

What is the value of z for the equation 1/4z = –7/8 + 1/8z? –3 –7 3 7

Answer 1

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