Solve z=x/4+a-3/4

$$z = \frac { x } { 4 } + a - 3 / 4$$

Solve for a

$$a=-\frac{x}{4}+z+\frac{3}{4}$$

Solution Steps

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

$$z=\frac{x-3}{4}+a$$

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

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

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

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

Subtract \frac{1}{4}x from both sides.

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

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

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

Solve for x

$$x=4z-4a+3$$

Steps for Solving Linear Equation

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

$$z=\frac{x-3}{4}+a$$

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

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

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

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

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

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

Subtract a from both sides.

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

The equation is in standard form.

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

Multiply both sides by 4.

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

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

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

Divide z+\frac{3}{4}-a by \frac{1}{4} by multiplying z+\frac{3}{4}-a by the reciprocal of \frac{1}{4}.

$$x=4z-4a+3$$