Solve 3x+x-1/2=x+1/4-2x-1/3

$$3 x + \frac { x - 1 } { 2 } = \frac { x + 1 } { 4 } - \frac { 2 x - 1 } { 3 }$$

Solve for x

$$x=\frac{13}{47}\approx 0.276595745$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,4,3.

$$36x+6\left(x-1\right)=3\left(x+1\right)-4\left(2x-1\right)$$

Use the distributive property to multiply 6 by x-1.

$$36x+6x-6=3\left(x+1\right)-4\left(2x-1\right)$$

Combine 36x and 6x to get 42x.

$$42x-6=3\left(x+1\right)-4\left(2x-1\right)$$

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

$$42x-6=3x+3-4\left(2x-1\right)$$

Use the distributive property to multiply -4 by 2x-1.

$$42x-6=3x+3-8x+4$$

Combine 3x and -8x to get -5x.

$$42x-6=-5x+3+4$$

Add 3 and 4 to get 7.

$$42x-6=-5x+7$$

Add 5x to both sides.

$$42x-6+5x=7$$

Combine 42x and 5x to get 47x.

$$47x-6=7$$

Add 6 to both sides.

$$47x=7+6$$

Add 7 and 6 to get 13.

$$47x=13$$

Divide both sides by 47.

$$x=\frac{13}{47}$$