Solve 1-4-3x/4=5x+3/b-x

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

Solve for b

$$b=\frac{20}{7}+\frac{12}{7x}$$

$$x\neq -\frac{3}{5}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b, the least common multiple of 4,b.

$$4b-b\left(4-3x\right)=4\left(5x+3\right)-x\times 4b$$

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

$$4b-\left(4b-3bx\right)=4\left(5x+3\right)-x\times 4b$$

To find the opposite of 4b-3bx, find the opposite of each term.

$$4b-4b+3bx=4\left(5x+3\right)-x\times 4b$$

Combine 4b and -4b to get 0.

$$3bx=4\left(5x+3\right)-x\times 4b$$

Use the distributive property to multiply 4 by 5x+3.

$$3bx=20x+12-x\times 4b$$

Multiply -1 and 4 to get -4.

$$3bx=20x+12-4xb$$

Add 4xb to both sides.

$$3bx+4xb=20x+12$$

Combine 3bx and 4xb to get 7bx.

$$7bx=20x+12$$

The equation is in standard form.

$$7xb=20x+12$$

Divide both sides by 7x.

$$\frac{7xb}{7x}=\frac{20x+12}{7x}$$

Dividing by 7x undoes the multiplication by 7x.

$$b=\frac{20x+12}{7x}$$

Divide 20x+12 by 7x.

$$b=\frac{20}{7}+\frac{12}{7x}$$

Variable b cannot be equal to 0.

$$b=\frac{20}{7}+\frac{12}{7x}\text{, }b\neq 0$$

Solve for x

$$x=\frac{12}{7b-20}$$

$$b\neq \frac{20}{7}\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4b, the least common multiple of 4,b.

$$4b-b\left(4-3x\right)=4\left(5x+3\right)-x\times 4b$$

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

$$4b-\left(4b-3bx\right)=4\left(5x+3\right)-x\times 4b$$

To find the opposite of 4b-3bx, find the opposite of each term.

$$4b-4b+3bx=4\left(5x+3\right)-x\times 4b$$

Combine 4b and -4b to get 0.

$$3bx=4\left(5x+3\right)-x\times 4b$$

Use the distributive property to multiply 4 by 5x+3.

$$3bx=20x+12-x\times 4b$$

Multiply -1 and 4 to get -4.

$$3bx=20x+12-4xb$$

Subtract 20x from both sides.

$$3bx-20x=12-4xb$$

Add 4xb to both sides.

$$3bx-20x+4xb=12$$

Combine 3bx and 4xb to get 7bx.

$$7bx-20x=12$$

Combine all terms containing x.

$$\left(7b-20\right)x=12$$

Divide both sides by -20+7b.

$$\frac{\left(7b-20\right)x}{7b-20}=\frac{12}{7b-20}$$

Dividing by -20+7b undoes the multiplication by -20+7b.

$$x=\frac{12}{7b-20}$$