Solve 3z-1/2=z-4/3

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

Solve for z

$$z=-\frac{5}{7}\approx -0.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(3z-1\right)=2\left(z-4\right)$$

Use the distributive property to multiply 3 by 3z-1.

$$9z-3=2\left(z-4\right)$$

Use the distributive property to multiply 2 by z-4.

$$9z-3=2z-8$$

Subtract 2z from both sides.

$$9z-3-2z=-8$$

Combine 9z and -2z to get 7z.

$$7z-3=-8$$

Add 3 to both sides.

$$7z=-8+3$$

Add -8 and 3 to get -5.

$$7z=-5$$

Divide both sides by 7.

$$z=\frac{-5}{7}$$

Fraction \frac{-5}{7} can be rewritten as -\frac{5}{7} by extracting the negative sign.

$$z=-\frac{5}{7}$$