Solve 2x-1/3-x/15-2(x+2)/10=2/3+frac{x-1}{2}

$$\frac { 2 x - 1 } { 3 } - \frac { x } { 15 } - \frac { 2 ( x + 2 ) } { 10 } = \frac { 2 } { 3 } + \frac { x - 1 } { 2 }$$

Solve for x

$$x=-9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,15,10,2.

$$10\left(2x-1\right)-2x-3\times 2\left(x+2\right)=20+15\left(x-1\right)$$

Use the distributive property to multiply 10 by 2x-1.

$$20x-10-2x-3\times 2\left(x+2\right)=20+15\left(x-1\right)$$

Combine 20x and -2x to get 18x.

$$18x-10-3\times 2\left(x+2\right)=20+15\left(x-1\right)$$

Multiply -3 and 2 to get -6.

$$18x-10-6\left(x+2\right)=20+15\left(x-1\right)$$

Use the distributive property to multiply -6 by x+2.

$$18x-10-6x-12=20+15\left(x-1\right)$$

Combine 18x and -6x to get 12x.

$$12x-10-12=20+15\left(x-1\right)$$

Subtract 12 from -10 to get -22.

$$12x-22=20+15\left(x-1\right)$$

Use the distributive property to multiply 15 by x-1.

$$12x-22=20+15x-15$$

Subtract 15 from 20 to get 5.

$$12x-22=5+15x$$

Subtract 15x from both sides.

$$12x-22-15x=5$$

Combine 12x and -15x to get -3x.

$$-3x-22=5$$

Add 22 to both sides.

$$-3x=5+22$$

Add 5 and 22 to get 27.

$$-3x=27$$

Divide both sides by -3.

$$x=\frac{27}{-3}$$

Divide 27 by -3 to get -9.

$$x=-9$$