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

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

Solve for x

$$x = -\frac{51}{10} = -5\frac{1}{10} = -5.1$$

Steps for Solving Linear Equation

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

$$6x-12\left(4-\frac{2x}{3}\right)=24x+3$$

Subtract 24x from both sides.

$$6x-12\left(4-\frac{2x}{3}\right)-24x=3$$

Multiply both sides of the equation by 3.

$$3\left(6x-12\left(4-\frac{2x}{3}\right)\right)-72x=9$$

Multiply both sides of the equation by 3.

$$9\left(6x-12\left(4-\frac{2x}{3}\right)\right)-216x=27$$

Use the distributive property to multiply -12 by 4-\frac{2x}{3}.

$$9\left(6x-48+12\times \frac{2x}{3}\right)-216x=27$$

Cancel out 3, the greatest common factor in 12 and 3.

$$9\left(6x-48+4\times 2x\right)-216x=27$$

Multiply 4 and 2 to get 8.

$$9\left(6x-48+8x\right)-216x=27$$

Combine 6x and 8x to get 14x.

$$9\left(14x-48\right)-216x=27$$

Use the distributive property to multiply 9 by 14x-48.

$$126x-432-216x=27$$

Combine 126x and -216x to get -90x.

$$-90x-432=27$$

Add 432 to both sides.

$$-90x=27+432$$

Add 27 and 432 to get 459.

$$-90x=459$$

Divide both sides by -90.

$$x=\frac{459}{-90}$$

Reduce the fraction \frac{459}{-90} to lowest terms by extracting and canceling out 9.

$$x=-\frac{51}{10}$$