Solve -1/6=2/5(x-1)-x+2/3-2x+3/6+frac{2}{5}

$$- \frac { 1 } { 6 } = \frac { 2 } { 5 } ( x - 1 ) - \frac { x + 2 } { 3 } - \frac { 2 x + 3 } { 6 } + \frac { 2 } { 5 }$$

Solve for x

$$x = -\frac{15}{4} = -3\frac{3}{4} = -3.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,5,3.

$$-5=12\left(x-1\right)-10\left(x+2\right)-5\left(2x+3\right)+12$$

Use the distributive property to multiply 12 by x-1.

$$-5=12x-12-10\left(x+2\right)-5\left(2x+3\right)+12$$

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

$$-5=12x-12-10x-20-5\left(2x+3\right)+12$$

Combine 12x and -10x to get 2x.

$$-5=2x-12-20-5\left(2x+3\right)+12$$

Subtract 20 from -12 to get -32.

$$-5=2x-32-5\left(2x+3\right)+12$$

Use the distributive property to multiply -5 by 2x+3.

$$-5=2x-32-10x-15+12$$

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

$$-5=-8x-32-15+12$$

Subtract 15 from -32 to get -47.

$$-5=-8x-47+12$$

Add -47 and 12 to get -35.

$$-5=-8x-35$$

Swap sides so that all variable terms are on the left hand side.

$$-8x-35=-5$$

Add 35 to both sides.

$$-8x=-5+35$$

Add -5 and 35 to get 30.

$$-8x=30$$

Divide both sides by -8.

$$x=\frac{30}{-8}$$

Reduce the fraction \frac{30}{-8} to lowest terms by extracting and canceling out 2.

$$x=-\frac{15}{4}$$