Solve d10x+8=7x-2

$$d 10 x + 8 = 7 x - 2$$

Solve for d_10

$$d_{10}=7-\frac{10}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 8 from both sides.

$$d_{10}x=7x-2-8$$

Subtract 8 from -2 to get -10.

$$d_{10}x=7x-10$$

The equation is in standard form.

$$xd_{10}=7x-10$$

Divide both sides by x.

$$\frac{xd_{10}}{x}=\frac{7x-10}{x}$$

Dividing by x undoes the multiplication by x.

$$d_{10}=\frac{7x-10}{x}$$

Divide 7x-10 by x.

$$d_{10}=7-\frac{10}{x}$$

Solve for x

$$x=-\frac{10}{d_{10}-7}$$

$$d_{10}\neq 7$$

Steps for Solving Linear Equation

Subtract 7x from both sides.

$$d_{10}x+8-7x=-2$$

Subtract 8 from both sides.

$$d_{10}x-7x=-2-8$$

Subtract 8 from -2 to get -10.

$$d_{10}x-7x=-10$$

Combine all terms containing x.

$$\left(d_{10}-7\right)x=-10$$

Divide both sides by d_{10}-7.

$$\frac{\left(d_{10}-7\right)x}{d_{10}-7}=-\frac{10}{d_{10}-7}$$

Dividing by d_{10}-7 undoes the multiplication by d_{10}-7.

$$x=-\frac{10}{d_{10}-7}$$