Solve 2(u-3)/4-2(u+4)/3=1+3u/2

$$\frac { 2 ( u - 3 ) } { 4 } - \frac { 2 ( u + 4 ) } { 3 } = 1 + \frac { 3 u } { 2 }$$

Solve for u

$$u = -\frac{31}{10} = -3\frac{1}{10} = -3.1$$

Steps for Solving Linear Equation

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

$$3\times 2\left(u-3\right)-4\times 2\left(u+4\right)=12+6\times 3u$$

Multiply 3 and 2 to get 6.

$$6\left(u-3\right)-4\times 2\left(u+4\right)=12+6\times 3u$$

Use the distributive property to multiply 6 by u-3.

$$6u-18-4\times 2\left(u+4\right)=12+6\times 3u$$

Multiply -4 and 2 to get -8.

$$6u-18-8\left(u+4\right)=12+6\times 3u$$

Use the distributive property to multiply -8 by u+4.

$$6u-18-8u-32=12+6\times 3u$$

Combine 6u and -8u to get -2u.

$$-2u-18-32=12+6\times 3u$$

Subtract 32 from -18 to get -50.

$$-2u-50=12+6\times 3u$$

Multiply 6 and 3 to get 18.

$$-2u-50=12+18u$$

Subtract 18u from both sides.

$$-2u-50-18u=12$$

Combine -2u and -18u to get -20u.

$$-20u-50=12$$

Add 50 to both sides.

$$-20u=12+50$$

Add 12 and 50 to get 62.

$$-20u=62$$

Divide both sides by -20.

$$u=\frac{62}{-20}$$

Reduce the fraction \frac{62}{-20} to lowest terms by extracting and canceling out 2.

$$u=-\frac{31}{10}$$