Solve 8x+5=bx-7

$$8 x + 5 = b x - 7$$

Solve for b

$$b=8+\frac{12}{x},x\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$bx-7=8x+5$$

Add 7 to both sides.

$$bx=8x+5+7$$

Add 5 and 7 to get 12.

$$bx=8x+12$$

The equation is in standard form.

$$xb=8x+12$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{8x+12}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{8x+12}{x}$$

Divide 8x+12 by x.

$$b=8+\frac{12}{x}$$

Solve for x

$$x=-\frac{12}{8-b},b\neq 8$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$8x+5-bx=-7$$

Subtract 5 from both sides.

$$8x-bx=-7-5$$

Subtract 5 from -7 to get -12.

$$8x-bx=-12$$

Combine all terms containing x.

$$\left(8-b\right)x=-12$$

Divide both sides by 8-b.

$$\frac{\left(8-b\right)x}{8-b}=\frac{-12}{8-b}$$

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

$$x=\frac{-12}{8-b}$$

Divide -12 by 8-b.

$$x=-\frac{12}{8-b}$$