Solve 3/4(z+8)=1/3(z-12)

$$\frac { 3 } { 4 } ( z + 8 ) = \frac { 1 } { 3 } ( z - 12 )$$

Solve for z

$$z=-24$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by z+8.

$$\frac{3}{4}z+\frac{3}{4}\times 8=\frac{1}{3}\left(z-12\right)$$

Express \frac{3}{4}\times 8 as a single fraction.

$$\frac{3}{4}z+\frac{3\times 8}{4}=\frac{1}{3}\left(z-12\right)$$

Multiply 3 and 8 to get 24.

$$\frac{3}{4}z+\frac{24}{4}=\frac{1}{3}\left(z-12\right)$$

Divide 24 by 4 to get 6.

$$\frac{3}{4}z+6=\frac{1}{3}\left(z-12\right)$$

Use the distributive property to multiply \frac{1}{3} by z-12.

$$\frac{3}{4}z+6=\frac{1}{3}z+\frac{1}{3}\left(-12\right)$$

Multiply \frac{1}{3} and -12 to get \frac{-12}{3}.

$$\frac{3}{4}z+6=\frac{1}{3}z+\frac{-12}{3}$$

Divide -12 by 3 to get -4.

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

Subtract \frac{1}{3}z from both sides.

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

Combine \frac{3}{4}z and -\frac{1}{3}z to get \frac{5}{12}z.

$$\frac{5}{12}z+6=-4$$

Subtract 6 from both sides.

$$\frac{5}{12}z=-4-6$$

Subtract 6 from -4 to get -10.

$$\frac{5}{12}z=-10$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$z=-10\times \frac{12}{5}$$

Express -10\times \frac{12}{5} as a single fraction.

$$z=\frac{-10\times 12}{5}$$

Multiply -10 and 12 to get -120.

$$z=\frac{-120}{5}$$

Divide -120 by 5 to get -24.

$$z=-24$$