Solve (x/4-3)+5x/6-5x/4=x-12/5-frac{x+3}{3}

$$( \frac { x } { 4 } - 3 ) + \frac { 5 x } { 6 } - \frac { 5 x } { 4 } = \frac { x - 12 } { 5 } - \frac { x + 3 } { 3 }$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 4,6,5,3.

$$15x-180+10\times 5x-15\times 5x=12\left(x-12\right)-20\left(x+3\right)$$

Multiply 10 and 5 to get 50.

$$15x-180+50x-15\times 5x=12\left(x-12\right)-20\left(x+3\right)$$

Combine 15x and 50x to get 65x.

$$65x-180-15\times 5x=12\left(x-12\right)-20\left(x+3\right)$$

Multiply -15 and 5 to get -75.

$$65x-180-75x=12\left(x-12\right)-20\left(x+3\right)$$

Combine 65x and -75x to get -10x.

$$-10x-180=12\left(x-12\right)-20\left(x+3\right)$$

Use the distributive property to multiply 12 by x-12.

$$-10x-180=12x-144-20\left(x+3\right)$$

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

$$-10x-180=12x-144-20x-60$$

Combine 12x and -20x to get -8x.

$$-10x-180=-8x-144-60$$

Subtract 60 from -144 to get -204.

$$-10x-180=-8x-204$$

Add 8x to both sides.

$$-10x-180+8x=-204$$

Combine -10x and 8x to get -2x.

$$-2x-180=-204$$

Add 180 to both sides.

$$-2x=-204+180$$

Add -204 and 180 to get -24.

$$-2x=-24$$

Divide both sides by -2.

$$x=\frac{-24}{-2}$$

Divide -24 by -2 to get 12.

$$x=12$$