Solve 3(x+5)div6+x-5=(4x-1)div3-(2x-2)div12

$$3 ( x + 5 ) \div 6 + x - 5 = ( 4 x - 1 ) \div 3 - ( 2 x - 2 ) \div 12$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

$$2\times 3\left(x+5\right)+12x-60=4\left(4x-1\right)-\left(2x-2\right)$$

Multiply 2 and 3 to get 6.

$$6\left(x+5\right)+12x-60=4\left(4x-1\right)-\left(2x-2\right)$$

Use the distributive property to multiply 6 by x+5.

$$6x+30+12x-60=4\left(4x-1\right)-\left(2x-2\right)$$

Combine 6x and 12x to get 18x.

$$18x+30-60=4\left(4x-1\right)-\left(2x-2\right)$$

Subtract 60 from 30 to get -30.

$$18x-30=4\left(4x-1\right)-\left(2x-2\right)$$

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

$$18x-30=16x-4-\left(2x-2\right)$$

To find the opposite of 2x-2, find the opposite of each term.

$$18x-30=16x-4-2x-\left(-2\right)$$

The opposite of -2 is 2.

$$18x-30=16x-4-2x+2$$

Combine 16x and -2x to get 14x.

$$18x-30=14x-4+2$$

Add -4 and 2 to get -2.

$$18x-30=14x-2$$

Subtract 14x from both sides.

$$18x-30-14x=-2$$

Combine 18x and -14x to get 4x.

$$4x-30=-2$$

Add 30 to both sides.

$$4x=-2+30$$

Add -2 and 30 to get 28.

$$4x=28$$

Divide both sides by 4.

$$x=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$x=7$$