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

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

Solve for x

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

Steps for Solving Linear Equation

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

$$\frac{1000}{24}\left(7x-1\right)=\frac{1}{0.018}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

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

$$\frac{125}{3}\left(7x-1\right)=\frac{1}{0.018}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

Use the distributive property to multiply \frac{125}{3} by 7x-1.

$$\frac{125}{3}\times 7x+\frac{125}{3}\left(-1\right)=\frac{1}{0.018}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

Express \frac{125}{3}\times 7 as a single fraction.

$$\frac{125\times 7}{3}x+\frac{125}{3}\left(-1\right)=\frac{1}{0.018}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

Multiply 125 and 7 to get 875.

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

Multiply \frac{125}{3} and -1 to get -\frac{125}{3}.

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

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

$$\frac{875}{3}x-\frac{125}{3}=\frac{1000}{18}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

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

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}\left(1-0.2x\right)-\frac{1}{0.012}\left(5x+1\right)$$

Use the distributive property to multiply \frac{500}{9} by 1-0.2x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}+\frac{500}{9}\left(-0.2\right)x-\frac{1}{0.012}\left(5x+1\right)$$

Convert decimal number -0.2 to fraction -\frac{2}{10}. Reduce the fraction -\frac{2}{10} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{500}{9} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{500\left(-1\right)}{9\times 5}.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}+\frac{-500}{45}x-\frac{1}{0.012}\left(5x+1\right)$$

Reduce the fraction \frac{-500}{45} to lowest terms by extracting and canceling out 5.

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

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

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{1000}{12}\left(5x+1\right)$$

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

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{250}{3}\left(5x+1\right)$$

Use the distributive property to multiply -\frac{250}{3} by 5x+1.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{250}{3}\times 5x-\frac{250}{3}$$

Express -\frac{250}{3}\times 5 as a single fraction.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x+\frac{-250\times 5}{3}x-\frac{250}{3}$$

Multiply -250 and 5 to get -1250.

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

Fraction \frac{-1250}{3} can be rewritten as -\frac{1250}{3} by extracting the negative sign.

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

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.

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

Multiply both sides by \frac{9}{6475}, the reciprocal of \frac{6475}{9}.

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

Multiply \frac{125}{9} times \frac{9}{6475} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 9 in both numerator and denominator.

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

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

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