Solve 7x-1/0.024=1-0.2x/0.018-5x+1/0.012

$$\frac { 7 x - 1 } { 0.024 } = \frac { 1 - 0.2 x } { 0.018 } - \frac { 5 x + 1 } { 0.012 }$$

Solve for x

$$x=\frac{5}{259}\approx 0.019305019$$

Steps for Solving Linear Equation

Divide each term of 7x-1 by 0.024 to get \frac{7x}{0.024}+\frac{-1}{0.024}.

$$\frac{7x}{0.024}+\frac{-1}{0.024}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Divide 7x by 0.024 to get \frac{875}{3}x.

$$\frac{875}{3}x+\frac{-1}{0.024}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Expand \frac{-1}{0.024} by multiplying both numerator and the denominator by 1000.

$$\frac{875}{3}x+\frac{-1000}{24}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Reduce the fraction \frac{-1000}{24} to lowest terms by extracting and canceling out 8.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Divide each term of 1-0.2x by 0.018 to get \frac{1}{0.018}+\frac{-0.2x}{0.018}.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1}{0.018}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Expand \frac{1}{0.018} by multiplying both numerator and the denominator by 1000.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1000}{18}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Reduce the fraction \frac{1000}{18} to lowest terms by extracting and canceling out 2.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Divide -0.2x by 0.018 to get -\frac{100}{9}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{5x+1}{0.012}$$

Divide each term of 5x+1 by 0.012 to get \frac{5x}{0.012}+\frac{1}{0.012}.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{5x}{0.012}+\frac{1}{0.012}\right)$$

Divide 5x by 0.012 to get \frac{1250}{3}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{1}{0.012}\right)$$

Expand \frac{1}{0.012} by multiplying both numerator and the denominator by 1000.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{1000}{12}\right)$$

Reduce the fraction \frac{1000}{12} to lowest terms by extracting and canceling out 4.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{250}{3}\right)$$

To find the opposite of \frac{1250}{3}x+\frac{250}{3}, find the opposite of each term.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{1250}{3}x-\frac{250}{3}$$

Combine -\frac{100}{9}x and -\frac{1250}{3}x to get -\frac{3850}{9}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{3850}{9}x-\frac{250}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{500}{9} and \frac{250}{3} to fractions with denominator 9.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{3850}{9}x-\frac{750}{9}$$

Since \frac{500}{9} and \frac{750}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500-750}{9}-\frac{3850}{9}x$$

Subtract 750 from 500 to get -250.

$$\frac{875}{3}x-\frac{125}{3}=-\frac{250}{9}-\frac{3850}{9}x$$

Add \frac{3850}{9}x to both sides.

$$\frac{875}{3}x-\frac{125}{3}+\frac{3850}{9}x=-\frac{250}{9}$$

Combine \frac{875}{3}x and \frac{3850}{9}x to get \frac{6475}{9}x.

$$\frac{6475}{9}x-\frac{125}{3}=-\frac{250}{9}$$

Add \frac{125}{3} to both sides.

$$\frac{6475}{9}x=-\frac{250}{9}+\frac{125}{3}$$

Least common multiple of 9 and 3 is 9. Convert -\frac{250}{9} and \frac{125}{3} to fractions with denominator 9.

$$\frac{6475}{9}x=-\frac{250}{9}+\frac{375}{9}$$

Since -\frac{250}{9} and \frac{375}{9} have the same denominator, add them by adding their numerators.

$$\frac{6475}{9}x=\frac{-250+375}{9}$$

Add -250 and 375 to get 125.

$$\frac{6475}{9}x=\frac{125}{9}$$

Divide both sides by \frac{6475}{9}.

$$x=\frac{\frac{125}{9}}{\frac{6475}{9}}$$

Express \frac{\frac{125}{9}}{\frac{6475}{9}} as a single fraction.

$$x=\frac{125}{9\times \frac{6475}{9}}$$

Multiply 9 and \frac{6475}{9} to get 6475.

$$x=\frac{125}{6475}$$

Reduce the fraction \frac{125}{6475} to lowest terms by extracting and canceling out 25.

$$x=\frac{5}{259}$$