Solve x+2/6-(11-x/3-1/4)=3x-4/12

$$\frac { x + 2 } { 6 } - ( \frac { 11 - x } { 3 } - \frac { 1 } { 4 } ) = \frac { 3 x - 4 } { 12 }$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

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

$$2\left(x+2\right)-12\left(\frac{11-x}{3}-\frac{1}{4}\right)=3x-4$$

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

$$2x+4-12\left(\frac{11-x}{3}-\frac{1}{4}\right)=3x-4$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{11-x}{3} times \frac{4}{4}. Multiply \frac{1}{4} times \frac{3}{3}.

$$2x+4-12\left(\frac{4\left(11-x\right)}{12}-\frac{3}{12}\right)=3x-4$$

Since \frac{4\left(11-x\right)}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$2x+4-12\times \frac{4\left(11-x\right)-3}{12}=3x-4$$

Do the multiplications in 4\left(11-x\right)-3.

$$2x+4-12\times \frac{44-4x-3}{12}=3x-4$$

Combine like terms in 44-4x-3.

$$2x+4-12\times \frac{41-4x}{12}=3x-4$$

Express 12\times \frac{41-4x}{12} as a single fraction.

$$2x+4-\frac{12\left(41-4x\right)}{12}=3x-4$$

Cancel out 12 and 12.

$$2x+4-\left(41-4x\right)=3x-4$$

To find the opposite of 41-4x, find the opposite of each term.

$$2x+4-41-\left(-4x\right)=3x-4$$

The opposite of -4x is 4x.

$$2x+4-41+4x=3x-4$$

Subtract 41 from 4 to get -37.

$$2x-37+4x=3x-4$$

Combine 2x and 4x to get 6x.

$$6x-37=3x-4$$

Subtract 3x from both sides.

$$6x-37-3x=-4$$

Combine 6x and -3x to get 3x.

$$3x-37=-4$$

Add 37 to both sides.

$$3x=-4+37$$

Add -4 and 37 to get 33.

$$3x=33$$

Divide both sides by 3.

$$x=\frac{33}{3}$$

Divide 33 by 3 to get 11.

$$x=11$$