Solve 1/3(3)+1/4(-1/2)+1/96z=0

$$\frac { 1 } { 3 } ( 3 ) + \frac { 1 } { 4 } ( \frac { - 1 } { 2 } ) + \frac { 1 } { 96 } z = 0$$

Solve for z

$$z=-84$$

Steps for Solving Linear Equation

Cancel out 3 and 3.

$$1+\frac{1}{4}\times \frac{-1}{2}+\frac{1}{96}z=0$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$1+\frac{1}{4}\left(-\frac{1}{2}\right)+\frac{1}{96}z=0$$

Multiply \frac{1}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\left(-1\right)}{4\times 2}+\frac{1}{96}z=0$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 2}.

$$1+\frac{-1}{8}+\frac{1}{96}z=0$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$1-\frac{1}{8}+\frac{1}{96}z=0$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{8}{8}-\frac{1}{8}+\frac{1}{96}z=0$$

Since \frac{8}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{8}+\frac{1}{96}z=0$$

Subtract 1 from 8 to get 7.

$$\frac{7}{8}+\frac{1}{96}z=0$$

Subtract \frac{7}{8} from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{96}z=-\frac{7}{8}$$

Multiply both sides by 96, the reciprocal of \frac{1}{96}.

$$z=-\frac{7}{8}\times 96$$

Express -\frac{7}{8}\times 96 as a single fraction.

$$z=\frac{-7\times 96}{8}$$

Multiply -7 and 96 to get -672.

$$z=\frac{-672}{8}$$

Divide -672 by 8 to get -84.

$$z=-84$$