Solve 3(x+6)div4=(4x-5)div6+(2x+2)div3

$$3(x+6) \div 4=(4x-5) \div 6+(2x+2) \div 3$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

$$3\times 3\left(x+6\right)=2\left(4x-5\right)+4\left(2x+2\right)$$

Multiply 3 and 3 to get 9.

$$9\left(x+6\right)=2\left(4x-5\right)+4\left(2x+2\right)$$

Use the distributive property to multiply 9 by x+6.

$$9x+54=2\left(4x-5\right)+4\left(2x+2\right)$$

Use the distributive property to multiply 2 by 4x-5.

$$9x+54=8x-10+4\left(2x+2\right)$$

Use the distributive property to multiply 4 by 2x+2.

$$9x+54=8x-10+8x+8$$

Combine 8x and 8x to get 16x.

$$9x+54=16x-10+8$$

Add -10 and 8 to get -2.

$$9x+54=16x-2$$

Subtract 16x from both sides.

$$9x+54-16x=-2$$

Combine 9x and -16x to get -7x.

$$-7x+54=-2$$

Subtract 54 from both sides.

$$-7x=-2-54$$

Subtract 54 from -2 to get -56.

$$-7x=-56$$

Divide both sides by -7.

$$x=\frac{-56}{-7}$$

Divide -56 by -7 to get 8.

$$x=8$$