Solve -x/4+-[15x-6(x+1)]/2=-x/2-(-2+x)-3x-1/6

$$- \frac { x } { 4 } + \frac { - [ 15 x - 6 ( x + 1 ) ] } { 2 } = \frac { - x } { 2 } - \frac { ( - 2 + x ) - 3 x - 1 } { 6 }$$

Solve for x

$$x=\frac{6}{11}\approx 0.545454545$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,2,6.

$$-3x+6\left(-\left(15x-6\left(x+1\right)\right)\right)=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

Use the distributive property to multiply -6 by x+1.

$$-3x+6\left(-\left(15x-6x-6\right)\right)=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

Combine 15x and -6x to get 9x.

$$-3x+6\left(-\left(9x-6\right)\right)=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

To find the opposite of 9x-6, find the opposite of each term.

$$-3x+6\left(-9x-\left(-6\right)\right)=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

The opposite of -6 is 6.

$$-3x+6\left(-9x+6\right)=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

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

$$-3x-54x+36=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

Combine -3x and -54x to get -57x.

$$-57x+36=6\left(-x\right)-2\left(-2+x-3x-1\right)$$

Combine x and -3x to get -2x.

$$-57x+36=6\left(-x\right)-2\left(-2-2x-1\right)$$

Subtract 1 from -2 to get -3.

$$-57x+36=6\left(-x\right)-2\left(-3-2x\right)$$

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

$$-57x+36=6\left(-x\right)+6+4x$$

Subtract 6\left(-x\right) from both sides.

$$-57x+36-6\left(-x\right)=6+4x$$

Subtract 4x from both sides.

$$-57x+36-6\left(-x\right)-4x=6$$

Multiply -1 and 6 to get -6.

$$-57x+36-6\left(-1\right)x-4x=6$$

Multiply -6 and -1 to get 6.

$$-57x+36+6x-4x=6$$

Combine -57x and 6x to get -51x.

$$-51x+36-4x=6$$

Combine -51x and -4x to get -55x.

$$-55x+36=6$$

Subtract 36 from both sides.

$$-55x=6-36$$

Subtract 36 from 6 to get -30.

$$-55x=-30$$

Divide both sides by -55.

$$x=\frac{-30}{-55}$$

Reduce the fraction \frac{-30}{-55} to lowest terms by extracting and canceling out -5.

$$x=\frac{6}{11}$$