Solve {l}{x-2/3-2x+1/6=3x-1/4-2x+1/2}

$$\left. \begin{array} { l } { \frac { x - 2 } { 3 } - \frac { 2 x + 1 } { 6 } = \frac { 3 x - 1 } { 4 } - \frac { 2 x + 1 } { 2 } } \end{array} \right.$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,6,4,2.

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

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

$$4x-8-2\left(2x+1\right)=3\left(3x-1\right)-6\left(2x+1\right)$$

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

$$4x-8-4x-2=3\left(3x-1\right)-6\left(2x+1\right)$$

Combine 4x and -4x to get 0.

$$-8-2=3\left(3x-1\right)-6\left(2x+1\right)$$

Subtract 2 from -8 to get -10.

$$-10=3\left(3x-1\right)-6\left(2x+1\right)$$

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

$$-10=9x-3-6\left(2x+1\right)$$

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

$$-10=9x-3-12x-6$$

Combine 9x and -12x to get -3x.

$$-10=-3x-3-6$$

Subtract 6 from -3 to get -9.

$$-10=-3x-9$$

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

$$-3x-9=-10$$

Add 9 to both sides.

$$-3x=-10+9$$

Add -10 and 9 to get -1.

$$-3x=-1$$

Divide both sides by -3.

$$x=\frac{-1}{-3}$$

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{3}$$