Solve -2x-2/4+3(2x-1)/2=x-1/3-1/4-frac{2x-5}{6}

$$- \frac { 2 x - 2 } { 4 } + \frac { 3 ( 2 x - 1 ) } { 2 } = \frac { x - 1 } { 3 } - \frac { 1 } { 4 } - \frac { 2 x - 5 } { 6 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,2,3,6.

$$-3\left(2x-2\right)+6\times 3\left(2x-1\right)=4\left(x-1\right)-3-2\left(2x-5\right)$$

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

$$-6x+6+6\times 3\left(2x-1\right)=4\left(x-1\right)-3-2\left(2x-5\right)$$

Multiply 6 and 3 to get 18.

$$-6x+6+18\left(2x-1\right)=4\left(x-1\right)-3-2\left(2x-5\right)$$

Use the distributive property to multiply 18 by 2x-1.

$$-6x+6+36x-18=4\left(x-1\right)-3-2\left(2x-5\right)$$

Combine -6x and 36x to get 30x.

$$30x+6-18=4\left(x-1\right)-3-2\left(2x-5\right)$$

Subtract 18 from 6 to get -12.

$$30x-12=4\left(x-1\right)-3-2\left(2x-5\right)$$

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

$$30x-12=4x-4-3-2\left(2x-5\right)$$

Subtract 3 from -4 to get -7.

$$30x-12=4x-7-2\left(2x-5\right)$$

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

$$30x-12=4x-7-4x+10$$

Combine 4x and -4x to get 0.

$$30x-12=-7+10$$

Add -7 and 10 to get 3.

$$30x-12=3$$

Add 12 to both sides.

$$30x=3+12$$

Add 3 and 12 to get 15.

$$30x=15$$

Divide both sides by 30.

$$x=\frac{15}{30}$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$x=\frac{1}{2}$$