Solve x-4/2-2x+5/3-1=x/6-x-4/2

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

Solve for x

$$x=40$$

Steps for Solving Linear Equation

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

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

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

$$3x-12-2\left(2x+5\right)-6=x-3\left(x-4\right)$$

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

$$3x-12-4x-10-6=x-3\left(x-4\right)$$

Combine 3x and -4x to get -x.

$$-x-12-10-6=x-3\left(x-4\right)$$

Subtract 10 from -12 to get -22.

$$-x-22-6=x-3\left(x-4\right)$$

Subtract 6 from -22 to get -28.

$$-x-28=x-3\left(x-4\right)$$

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

$$-x-28=x-3x+12$$

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

$$-x-28=-2x+12$$

Add 2x to both sides.

$$-x-28+2x=12$$

Combine -x and 2x to get x.

$$x-28=12$$

Add 28 to both sides.

$$x=12+28$$

Add 12 and 28 to get 40.

$$x=40$$