Solve 1/4z+(z-6)=2/3(z-2)

$$\frac { 1 } { 4 } z + ( z - 6 ) = \frac { 2 } { 3 } ( z - 2 )$$

Solve for z

$$z=8$$

Steps for Solving Linear Equation

Combine \frac{1}{4}z and z to get \frac{5}{4}z.

$$\frac{5}{4}z-6=\frac{2}{3}\left(z-2\right)$$

Use the distributive property to multiply \frac{2}{3} by z-2.

$$\frac{5}{4}z-6=\frac{2}{3}z+\frac{2}{3}\left(-2\right)$$

Express \frac{2}{3}\left(-2\right) as a single fraction.

$$\frac{5}{4}z-6=\frac{2}{3}z+\frac{2\left(-2\right)}{3}$$

Multiply 2 and -2 to get -4.

$$\frac{5}{4}z-6=\frac{2}{3}z+\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{5}{4}z-6=\frac{2}{3}z-\frac{4}{3}$$

Subtract \frac{2}{3}z from both sides.

$$\frac{5}{4}z-6-\frac{2}{3}z=-\frac{4}{3}$$

Combine \frac{5}{4}z and -\frac{2}{3}z to get \frac{7}{12}z.

$$\frac{7}{12}z-6=-\frac{4}{3}$$

Add 6 to both sides.

$$\frac{7}{12}z=-\frac{4}{3}+6$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{7}{12}z=-\frac{4}{3}+\frac{18}{3}$$

Since -\frac{4}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}z=\frac{-4+18}{3}$$

Add -4 and 18 to get 14.

$$\frac{7}{12}z=\frac{14}{3}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$z=\frac{14}{3}\times \frac{12}{7}$$

Multiply \frac{14}{3} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$z=\frac{14\times 12}{3\times 7}$$

Do the multiplications in the fraction \frac{14\times 12}{3\times 7}.

$$z=\frac{168}{21}$$

Divide 168 by 21 to get 8.

$$z=8$$