Solve 5x-7=bx+9

$$5 x - 7 = b x + 9$$

Solve for b

$$b=5-\frac{16}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$bx+9=5x-7$$

Subtract 9 from both sides.

$$bx=5x-7-9$$

Subtract 9 from -7 to get -16.

$$bx=5x-16$$

The equation is in standard form.

$$xb=5x-16$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{5x-16}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{5x-16}{x}$$

Divide 5x-16 by x.

$$b=5-\frac{16}{x}$$

Solve for x

$$x=\frac{16}{5-b}$$

$$b\neq 5$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$5x-7-bx=9$$

Add 7 to both sides.

$$5x-bx=9+7$$

Add 9 and 7 to get 16.

$$5x-bx=16$$

Combine all terms containing x.

$$\left(5-b\right)x=16$$

Divide both sides by 5-b.

$$\frac{\left(5-b\right)x}{5-b}=\frac{16}{5-b}$$

Dividing by 5-b undoes the multiplication by 5-b.

$$x=\frac{16}{5-b}$$