Solve 3x+1/3=x-3/6+5/12

$$\frac { 3 x + 1 } { 3 } = \frac { x - 3 } { 6 } + \frac { 5 } { 12 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,6,12.

$$4\left(3x+1\right)=2\left(x-3\right)+5$$

Use the distributive property to multiply 4 by 3x+1.

$$12x+4=2\left(x-3\right)+5$$

Use the distributive property to multiply 2 by x-3.

$$12x+4=2x-6+5$$

Add -6 and 5 to get -1.

$$12x+4=2x-1$$

Subtract 2x from both sides.

$$12x+4-2x=-1$$

Combine 12x and -2x to get 10x.

$$10x+4=-1$$

Subtract 4 from both sides.

$$10x=-1-4$$

Subtract 4 from -1 to get -5.

$$10x=-5$$

Divide both sides by 10.

$$x=\frac{-5}{10}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{1}{2}$$