Solve 2[x-1/2-2x-1]-13x-12/24-3x-2/6+4x=2

$$2 [ \frac { x - 1 } { 2 } - 2 x - 1 ] - \frac { 13 x - 12 } { 24 } - \frac { 3 x - 2 } { 6 } + 4 x = 2$$

Solve for x

$$x=-100$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 2,24,6.

$$48\left(\frac{x-1}{2}-2x-1\right)-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

Use the distributive property to multiply 48 by \frac{x-1}{2}-2x-1.

$$48\times \frac{x-1}{2}-96x-48-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

Cancel out 2, the greatest common factor in 48 and 2.

$$24\left(x-1\right)-96x-48-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

Use the distributive property to multiply 24 by x-1.

$$24x-24-96x-48-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

Combine 24x and -96x to get -72x.

$$-72x-24-48-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

Subtract 48 from -24 to get -72.

$$-72x-72-\left(13x-12\right)-4\left(3x-2\right)+96x=48$$

To find the opposite of 13x-12, find the opposite of each term.

$$-72x-72-13x-\left(-12\right)-4\left(3x-2\right)+96x=48$$

The opposite of -12 is 12.

$$-72x-72-13x+12-4\left(3x-2\right)+96x=48$$

Combine -72x and -13x to get -85x.

$$-85x-72+12-4\left(3x-2\right)+96x=48$$

Add -72 and 12 to get -60.

$$-85x-60-4\left(3x-2\right)+96x=48$$

Use the distributive property to multiply -4 by 3x-2.

$$-85x-60-12x+8+96x=48$$

Combine -85x and -12x to get -97x.

$$-97x-60+8+96x=48$$

Add -60 and 8 to get -52.

$$-97x-52+96x=48$$

Combine -97x and 96x to get -x.

$$-x-52=48$$

Add 52 to both sides.

$$-x=48+52$$

Add 48 and 52 to get 100.

$$-x=100$$

Multiply both sides by -1.

$$x=-100$$