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

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

Solve for x

$$x = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

Steps for Solving Linear Equation

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

$$6\left(2x-1\right)-4\left(3x-1\right)=12+3\left(x-1\right)$$

Use the distributive property to multiply 6 by 2x-1.

$$12x-6-4\left(3x-1\right)=12+3\left(x-1\right)$$

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

$$12x-6-12x+4=12+3\left(x-1\right)$$

Combine 12x and -12x to get 0.

$$-6+4=12+3\left(x-1\right)$$

Add -6 and 4 to get -2.

$$-2=12+3\left(x-1\right)$$

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

$$-2=12+3x-3$$

Subtract 3 from 12 to get 9.

$$-2=9+3x$$

Swap sides so that all variable terms are on the left hand side.

$$9+3x=-2$$

Subtract 9 from both sides.

$$3x=-2-9$$

Subtract 9 from -2 to get -11.

$$3x=-11$$

Divide both sides by 3.

$$x=\frac{-11}{3}$$

Fraction \frac{-11}{3} can be rewritten as -\frac{11}{3} by extracting the negative sign.

$$x=-\frac{11}{3}$$