Solve x=z/2-3/4

$$x = \frac { z } { 2 } - \frac { 3 } { 4 }$$

Solve for x

$$x=\frac{z}{2}-\frac{3}{4}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{z}{2} times \frac{2}{2}.

$$x=\frac{2z}{4}-\frac{3}{4}$$

Since \frac{2z}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{2z-3}{4}$$

Divide each term of 2z-3 by 4 to get \frac{1}{2}z-\frac{3}{4}.

$$x=\frac{1}{2}z-\frac{3}{4}$$

Solve for z

$$z=2x+\frac{3}{2}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{z}{2} times \frac{2}{2}.

$$x=\frac{2z}{4}-\frac{3}{4}$$

Since \frac{2z}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{2z-3}{4}$$

Divide each term of 2z-3 by 4 to get \frac{1}{2}z-\frac{3}{4}.

$$x=\frac{1}{2}z-\frac{3}{4}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}z-\frac{3}{4}=x$$

Add \frac{3}{4} to both sides.

$$\frac{1}{2}z=x+\frac{3}{4}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}z}{\frac{1}{2}}=\frac{x+\frac{3}{4}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$z=\frac{x+\frac{3}{4}}{\frac{1}{2}}$$

Divide x+\frac{3}{4} by \frac{1}{2} by multiplying x+\frac{3}{4} by the reciprocal of \frac{1}{2}.

$$z=2x+\frac{3}{2}$$