Solve x-u-1/3=u-1-u/2

$$x - \frac { u - 1 } { 3 } = u - \frac { 1 - u } { 2 }$$

Solve for u

$$u=\frac{6x+5}{11}$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply -2 by u-1.

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

Use the distributive property to multiply -3 by 1-u.

$$6x-2u+2=6u-3+3u$$

Combine 6u and 3u to get 9u.

$$6x-2u+2=9u-3$$

Subtract 9u from both sides.

$$6x-2u+2-9u=-3$$

Combine -2u and -9u to get -11u.

$$6x-11u+2=-3$$

Subtract 6x from both sides.

$$-11u+2=-3-6x$$

Subtract 2 from both sides.

$$-11u=-3-6x-2$$

Subtract 2 from -3 to get -5.

$$-11u=-5-6x$$

The equation is in standard form.

$$-11u=-6x-5$$

Divide both sides by -11.

$$\frac{-11u}{-11}=\frac{-6x-5}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$u=\frac{-6x-5}{-11}$$

Divide -5-6x by -11.

$$u=\frac{6x+5}{11}$$

Solve for x

$$x=\frac{11u-5}{6}$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply -2 by u-1.

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

Use the distributive property to multiply -3 by 1-u.

$$6x-2u+2=6u-3+3u$$

Combine 6u and 3u to get 9u.

$$6x-2u+2=9u-3$$

Add 2u to both sides.

$$6x+2=9u-3+2u$$

Combine 9u and 2u to get 11u.

$$6x+2=11u-3$$

Subtract 2 from both sides.

$$6x=11u-3-2$$

Subtract 2 from -3 to get -5.

$$6x=11u-5$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{11u-5}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{11u-5}{6}$$