Solve M=5-5/10+x-80

$$M = \frac { 5 - 5 } { 10 + x } - 80$$

Solve for M

$$M=-80$$

$$x\neq -10$$

Steps for Solving Linear Equation

Subtract 5 from 5 to get 0.

$$M=\frac{0}{10+x}-80$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 80 times \frac{10+x}{10+x}.

$$M=\frac{0}{10+x}-\frac{80\left(10+x\right)}{10+x}$$

Since \frac{0}{10+x} and \frac{80\left(10+x\right)}{10+x} have the same denominator, subtract them by subtracting their numerators.

$$M=\frac{0-80\left(10+x\right)}{10+x}$$

Do the multiplications in 0-80\left(10+x\right).

$$M=\frac{-800-80x}{10+x}$$

Factor the expressions that are not already factored in \frac{-800-80x}{10+x}.

$$M=\frac{80\left(-x-10\right)}{x+10}$$

Extract the negative sign in -10-x.

$$M=\frac{-80\left(x+10\right)}{x+10}$$

Cancel out x+10 in both numerator and denominator.

$$M=-80$$

Solve for x

$$x\neq -10$$

$$M=-80\text{ and }x\neq -10$$

Steps for Solving Linear Equation

Variable x cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by x+10.

$$M\left(x+10\right)=5-5+\left(x+10\right)\left(-80\right)$$

Use the distributive property to multiply M by x+10.

$$Mx+10M=5-5+\left(x+10\right)\left(-80\right)$$

Subtract 5 from 5 to get 0.

$$Mx+10M=\left(x+10\right)\left(-80\right)$$

Use the distributive property to multiply x+10 by -80.

$$Mx+10M=-80x-800$$

Add 80x to both sides.

$$Mx+10M+80x=-800$$

Subtract 10M from both sides.

$$Mx+80x=-800-10M$$

Combine all terms containing x.

$$\left(M+80\right)x=-800-10M$$

The equation is in standard form.

$$\left(M+80\right)x=-10M-800$$

Divide both sides by M+80.

$$\frac{\left(M+80\right)x}{M+80}=\frac{-10M-800}{M+80}$$

Dividing by M+80 undoes the multiplication by M+80.

$$x=\frac{-10M-800}{M+80}$$

Divide -800-10M by M+80.

$$x=-10$$

Variable x cannot be equal to -10.

$$x\in \emptyset$$