Solve 5(x+2)/12+4/9-22-x/36=3x-20/1-frac{8x}{12}-frac{20-3}{18}

$$\frac { 5 ( x + 2 ) } { 12 } + \frac { 4 } { 9 } - \frac { 22 - x } { 36 } = \frac { 3 x - 20 } { 1 } - \frac { 8 x } { 12 } - \frac { 20 - 3 } { 18 }$$

Solve for x

$$x = \frac{389}{34} = 11\frac{15}{34} \approx 11.441176471$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 12,9,36,18.

$$3\times 5\left(x+2\right)+16-\left(22-x\right)=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Multiply 3 and 5 to get 15.

$$15\left(x+2\right)+16-\left(22-x\right)=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Use the distributive property to multiply 15 by x+2.

$$15x+30+16-\left(22-x\right)=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Add 30 and 16 to get 46.

$$15x+46-\left(22-x\right)=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

To find the opposite of 22-x, find the opposite of each term.

$$15x+46-22-\left(-x\right)=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

The opposite of -x is x.

$$15x+46-22+x=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Subtract 22 from 46 to get 24.

$$15x+24+x=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Combine 15x and x to get 16x.

$$16x+24=36\left(3x-20\right)-3\times 8x-2\left(20-3\right)$$

Use the distributive property to multiply 36 by 3x-20.

$$16x+24=108x-720-3\times 8x-2\left(20-3\right)$$

Multiply -3 and 8 to get -24.

$$16x+24=108x-720-24x-2\left(20-3\right)$$

Combine 108x and -24x to get 84x.

$$16x+24=84x-720-2\left(20-3\right)$$

Subtract 3 from 20 to get 17.

$$16x+24=84x-720-2\times 17$$

Multiply -2 and 17 to get -34.

$$16x+24=84x-720-34$$

Subtract 34 from -720 to get -754.

$$16x+24=84x-754$$

Subtract 84x from both sides.

$$16x+24-84x=-754$$

Combine 16x and -84x to get -68x.

$$-68x+24=-754$$

Subtract 24 from both sides.

$$-68x=-754-24$$

Subtract 24 from -754 to get -778.

$$-68x=-778$$

Divide both sides by -68.

$$x=\frac{-778}{-68}$$

Reduce the fraction \frac{-778}{-68} to lowest terms by extracting and canceling out -2.

$$x=\frac{389}{34}$$