Solve 2x-1/3-4-x/12=3x-22/6+5

$$\frac { 2 x - 1 } { 3 } - \frac { 4 - x } { 12 } = \frac { 3 x - 22 } { 6 } + 5$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

$$4\left(2x-1\right)-\left(4-x\right)=2\left(3x-22\right)+60$$

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

$$8x-4-\left(4-x\right)=2\left(3x-22\right)+60$$

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

$$8x-4-4-\left(-x\right)=2\left(3x-22\right)+60$$

The opposite of -x is x.

$$8x-4-4+x=2\left(3x-22\right)+60$$

Subtract 4 from -4 to get -8.

$$8x-8+x=2\left(3x-22\right)+60$$

Combine 8x and x to get 9x.

$$9x-8=2\left(3x-22\right)+60$$

Use the distributive property to multiply 2 by 3x-22.

$$9x-8=6x-44+60$$

Add -44 and 60 to get 16.

$$9x-8=6x+16$$

Subtract 6x from both sides.

$$9x-8-6x=16$$

Combine 9x and -6x to get 3x.

$$3x-8=16$$

Add 8 to both sides.

$$3x=16+8$$

Add 16 and 8 to get 24.

$$3x=24$$

Divide both sides by 3.

$$x=\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$x=8$$