Solve 3(2x+2)/10-7(2x-5)/15-x-6/6=29/15

$$\frac { 3 ( 2 x + 2 ) } { 10 } - \frac { 7 ( 2 x - 5 ) } { 15 } - \frac { x - 6 } { 6 } = \frac { 29 } { 15 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 10,15,6.

$$3\times 3\left(2x+2\right)-2\times 7\left(2x-5\right)-5\left(x-6\right)=58$$

Multiply 3 and 3 to get 9.

$$9\left(2x+2\right)-2\times 7\left(2x-5\right)-5\left(x-6\right)=58$$

Use the distributive property to multiply 9 by 2x+2.

$$18x+18-2\times 7\left(2x-5\right)-5\left(x-6\right)=58$$

Multiply -2 and 7 to get -14.

$$18x+18-14\left(2x-5\right)-5\left(x-6\right)=58$$

Use the distributive property to multiply -14 by 2x-5.

$$18x+18-28x+70-5\left(x-6\right)=58$$

Combine 18x and -28x to get -10x.

$$-10x+18+70-5\left(x-6\right)=58$$

Add 18 and 70 to get 88.

$$-10x+88-5\left(x-6\right)=58$$

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

$$-10x+88-5x+30=58$$

Combine -10x and -5x to get -15x.

$$-15x+88+30=58$$

Add 88 and 30 to get 118.

$$-15x+118=58$$

Subtract 118 from both sides.

$$-15x=58-118$$

Subtract 118 from 58 to get -60.

$$-15x=-60$$

Divide both sides by -15.

$$x=\frac{-60}{-15}$$

Divide -60 by -15 to get 4.

$$x=4$$