Solve 0.1x-0.2/0.01-6.5=0.02-2x/0.02-7.5

$$\frac { 0.1 x - 0.2 } { 0.01 } - 6.5 = \frac { 0.02 - 2 x } { 0.02 } - 7.5$$

Solve for x

$$x=\frac{2}{11}\approx 0.181818182$$

Steps for Solving Linear Equation

Divide each term of 0.1x-0.2 by 0.01 to get \frac{0.1x}{0.01}+\frac{-0.2}{0.01}.

$$\frac{0.1x}{0.01}+\frac{-0.2}{0.01}-6.5=\frac{0.02-2x}{0.02}-7.5$$

Divide 0.1x by 0.01 to get 10x.

$$10x+\frac{-0.2}{0.01}-6.5=\frac{0.02-2x}{0.02}-7.5$$

Expand \frac{-0.2}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$10x-20-6.5=\frac{0.02-2x}{0.02}-7.5$$

Subtract 6.5 from -20 to get -26.5.

$$10x-26.5=\frac{0.02-2x}{0.02}-7.5$$

Divide each term of 0.02-2x by 0.02 to get \frac{0.02}{0.02}+\frac{-2x}{0.02}.

$$10x-26.5=\frac{0.02}{0.02}+\frac{-2x}{0.02}-7.5$$

Divide 0.02 by 0.02 to get 1.

$$10x-26.5=1+\frac{-2x}{0.02}-7.5$$

Divide -2x by 0.02 to get -100x.

$$10x-26.5=1-100x-7.5$$

Subtract 7.5 from 1 to get -6.5.

$$10x-26.5=-6.5-100x$$

Add 100x to both sides.

$$10x-26.5+100x=-6.5$$

Combine 10x and 100x to get 110x.

$$110x-26.5=-6.5$$

Add 26.5 to both sides.

$$110x=-6.5+26.5$$

Add -6.5 and 26.5 to get 20.

$$110x=20$$

Divide both sides by 110.

$$x=\frac{20}{110}$$

Reduce the fraction \frac{20}{110} to lowest terms by extracting and canceling out 10.

$$x=\frac{2}{11}$$