Solve -x/100=32-(x-8)/212-32

$$\frac{ -x }{ 100 } = \frac{ 32-(x-8) }{ 212-32 }$$

Solve for x

$$x=-50$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100.

$$-x=\frac{5}{9}\left(32-\left(x-8\right)\right)$$

To find the opposite of x-8, find the opposite of each term.

$$-x=\frac{5}{9}\left(32-x-\left(-8\right)\right)$$

The opposite of -8 is 8.

$$-x=\frac{5}{9}\left(32-x+8\right)$$

Add 32 and 8 to get 40.

$$-x=\frac{5}{9}\left(40-x\right)$$

Use the distributive property to multiply \frac{5}{9} by 40-x.

$$-x=\frac{5}{9}\times 40+\frac{5}{9}\left(-1\right)x$$

Express \frac{5}{9}\times 40 as a single fraction.

$$-x=\frac{5\times 40}{9}+\frac{5}{9}\left(-1\right)x$$

Multiply 5 and 40 to get 200.

$$-x=\frac{200}{9}+\frac{5}{9}\left(-1\right)x$$

Multiply \frac{5}{9} and -1 to get -\frac{5}{9}.

$$-x=\frac{200}{9}-\frac{5}{9}x$$

Add \frac{5}{9}x to both sides.

$$-x+\frac{5}{9}x=\frac{200}{9}$$

Combine -x and \frac{5}{9}x to get -\frac{4}{9}x.

$$-\frac{4}{9}x=\frac{200}{9}$$

Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.

$$x=\frac{200}{9}\left(-\frac{9}{4}\right)$$

Multiply \frac{200}{9} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{200\left(-9\right)}{9\times 4}$$

Do the multiplications in the fraction \frac{200\left(-9\right)}{9\times 4}.

$$x=\frac{-1800}{36}$$

Divide -1800 by 36 to get -50.

$$x=-50$$