Solve x+7-ux/3=11/6-5x/8

$$x + 7 - \frac { u x } { 3 } = \frac { 11 } { 6 } - \frac { 5 x } { 8 }$$

Solve for u

$$u=\frac{39}{8}+\frac{31}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 3,6,8.

$$24x+168-8ux=44-3\times 5x$$

Multiply -3 and 5 to get -15.

$$24x+168-8ux=44-15x$$

Subtract 24x from both sides.

$$168-8ux=44-15x-24x$$

Combine -15x and -24x to get -39x.

$$168-8ux=44-39x$$

Subtract 168 from both sides.

$$-8ux=44-39x-168$$

Subtract 168 from 44 to get -124.

$$-8ux=-124-39x$$

The equation is in standard form.

$$\left(-8x\right)u=-39x-124$$

Divide both sides by -8x.

$$\frac{\left(-8x\right)u}{-8x}=\frac{-39x-124}{-8x}$$

Dividing by -8x undoes the multiplication by -8x.

$$u=\frac{-39x-124}{-8x}$$

Divide -124-39x by -8x.

$$u=\frac{39}{8}+\frac{31}{2x}$$

Solve for x

$$x=-\frac{124}{39-8u}$$

$$u\neq \frac{39}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 3,6,8.

$$24x+168-8ux=44-3\times 5x$$

Multiply -3 and 5 to get -15.

$$24x+168-8ux=44-15x$$

Add 15x to both sides.

$$24x+168-8ux+15x=44$$

Combine 24x and 15x to get 39x.

$$39x+168-8ux=44$$

Subtract 168 from both sides.

$$39x-8ux=44-168$$

Subtract 168 from 44 to get -124.

$$39x-8ux=-124$$

Combine all terms containing x.

$$\left(39-8u\right)x=-124$$

Divide both sides by 39-8u.

$$\frac{\left(39-8u\right)x}{39-8u}=-\frac{124}{39-8u}$$

Dividing by 39-8u undoes the multiplication by 39-8u.

$$x=-\frac{124}{39-8u}$$