Solve 0.9-9x/1.2-1.2-3x/0.2=5x+1/0.3

$$\frac { 0.9 - 9 x } { 1.2 } - \frac { 1.2 - 3 x } { 0.2 } = \frac { 5 x + 1 } { 0.3 }$$

Solve for x

$$x=-\frac{103}{110}\approx -0.936363636$$

Steps for Solving Linear Equation

Divide each term of 0.9-9x by 1.2 to get \frac{0.9}{1.2}+\frac{-9x}{1.2}.

$$\frac{0.9}{1.2}+\frac{-9x}{1.2}-\frac{1.2-3x}{0.2}=\frac{5x+1}{0.3}$$

Expand \frac{0.9}{1.2} by multiplying both numerator and the denominator by 10.

$$\frac{9}{12}+\frac{-9x}{1.2}-\frac{1.2-3x}{0.2}=\frac{5x+1}{0.3}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}+\frac{-9x}{1.2}-\frac{1.2-3x}{0.2}=\frac{5x+1}{0.3}$$

Divide -9x by 1.2 to get -7.5x.

$$\frac{3}{4}-7.5x-\frac{1.2-3x}{0.2}=\frac{5x+1}{0.3}$$

Divide each term of 1.2-3x by 0.2 to get \frac{1.2}{0.2}+\frac{-3x}{0.2}.

$$\frac{3}{4}-7.5x-\left(\frac{1.2}{0.2}+\frac{-3x}{0.2}\right)=\frac{5x+1}{0.3}$$

Expand \frac{1.2}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{3}{4}-7.5x-\left(\frac{12}{2}+\frac{-3x}{0.2}\right)=\frac{5x+1}{0.3}$$

Divide 12 by 2 to get 6.

$$\frac{3}{4}-7.5x-\left(6+\frac{-3x}{0.2}\right)=\frac{5x+1}{0.3}$$

Divide -3x by 0.2 to get -15x.

$$\frac{3}{4}-7.5x-\left(6-15x\right)=\frac{5x+1}{0.3}$$

To find the opposite of 6-15x, find the opposite of each term.

$$\frac{3}{4}-7.5x-6-\left(-15x\right)=\frac{5x+1}{0.3}$$

The opposite of -15x is 15x.

$$\frac{3}{4}-7.5x-6+15x=\frac{5x+1}{0.3}$$

Convert 6 to fraction \frac{24}{4}.

$$\frac{3}{4}-7.5x-\frac{24}{4}+15x=\frac{5x+1}{0.3}$$

Since \frac{3}{4} and \frac{24}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-24}{4}-7.5x+15x=\frac{5x+1}{0.3}$$

Subtract 24 from 3 to get -21.

$$-\frac{21}{4}-7.5x+15x=\frac{5x+1}{0.3}$$

Combine -7.5x and 15x to get 7.5x.

$$-\frac{21}{4}+7.5x=\frac{5x+1}{0.3}$$

Divide each term of 5x+1 by 0.3 to get \frac{5x}{0.3}+\frac{1}{0.3}.

$$-\frac{21}{4}+7.5x=\frac{5x}{0.3}+\frac{1}{0.3}$$

Divide 5x by 0.3 to get \frac{50}{3}x.

$$-\frac{21}{4}+7.5x=\frac{50}{3}x+\frac{1}{0.3}$$

Expand \frac{1}{0.3} by multiplying both numerator and the denominator by 10.

$$-\frac{21}{4}+7.5x=\frac{50}{3}x+\frac{10}{3}$$

Subtract \frac{50}{3}x from both sides.

$$-\frac{21}{4}+7.5x-\frac{50}{3}x=\frac{10}{3}$$

Combine 7.5x and -\frac{50}{3}x to get -\frac{55}{6}x.

$$-\frac{21}{4}-\frac{55}{6}x=\frac{10}{3}$$

Add \frac{21}{4} to both sides.

$$-\frac{55}{6}x=\frac{10}{3}+\frac{21}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{21}{4} to fractions with denominator 12.

$$-\frac{55}{6}x=\frac{40}{12}+\frac{63}{12}$$

Since \frac{40}{12} and \frac{63}{12} have the same denominator, add them by adding their numerators.

$$-\frac{55}{6}x=\frac{40+63}{12}$$

Add 40 and 63 to get 103.

$$-\frac{55}{6}x=\frac{103}{12}$$

Divide both sides by -\frac{55}{6}.

$$x=\frac{\frac{103}{12}}{-\frac{55}{6}}$$

Express \frac{\frac{103}{12}}{-\frac{55}{6}} as a single fraction.

$$x=\frac{103}{12\left(-\frac{55}{6}\right)}$$

Multiply 12 and -\frac{55}{6} to get -110.

$$x=\frac{103}{-110}$$

Fraction \frac{103}{-110} can be rewritten as -\frac{103}{110} by extracting the negative sign.

$$x=-\frac{103}{110}$$