Answer:
[tex]\boxed {z = 6}[/tex]
Step-by-step explanation:
Solve for the value of [tex]z[/tex]:
[tex]\frac{1}{4} = \frac{1}{12} + \frac{1}{z}[/tex]
-The variable [tex]z[/tex] cannot equal to [tex]0[/tex] since division by zero is undefined. SO, you multiply both sides by [tex]12z[/tex], which is the least common multiple of [tex]4[/tex], [tex]12[/tex], and [tex]z[/tex]:
[tex]3z = 12z \times (\frac{1}{12}) + 12[/tex]
[tex]3z = z + 12[/tex]
-Take [tex]-z[/tex] and subtract it from [tex]3z[/tex]:
[tex]3z - z = z - z + 12[/tex]
[tex]2z = 12[/tex]
-Divide both sides by [tex]2[/tex]:
[tex]\frac{2z}{2} = \frac{12}{2}[/tex]
[tex]\boxed {z = 6}[/tex]
So, the value of [tex]z[/tex] of [tex]6[/tex].
