Solve 3x-1/2-2x+1/3=3-41/6

$$\frac{ 3x-1 }{ 2 } - \frac{ 2x+1 }{ 3 } = \frac{ 3-41 }{ 6 }$$

Solve for x

$$x = -\frac{33}{5} = -6\frac{3}{5} = -6.6$$

Steps for Solving Linear Equation

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

$$3\left(3x-1\right)-2\left(2x+1\right)=3-41$$

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

$$9x-3-2\left(2x+1\right)=3-41$$

Use the distributive property to multiply -2 by 2x+1.

$$9x-3-4x-2=3-41$$

Combine 9x and -4x to get 5x.

$$5x-3-2=3-41$$

Subtract 2 from -3 to get -5.

$$5x-5=3-41$$

Subtract 41 from 3 to get -38.

$$5x-5=-38$$

Add 5 to both sides.

$$5x=-38+5$$

Add -38 and 5 to get -33.

$$5x=-33$$

Divide both sides by 5.

$$x=\frac{-33}{5}$$

Fraction \frac{-33}{5} can be rewritten as -\frac{33}{5} by extracting the negative sign.

$$x=-\frac{33}{5}$$