Solve 1/24(7x-1)=1/1.8(0.1-0.2x)-1/12(5x+1)

$$\frac{ 1 }{ 24 } (7x-1)= \frac{ 1 }{ 1.8 } (0.1-0.2x)- \frac{ 1 }{ 12 } (5x+1)$$

Solve for x

$$x=\frac{1}{59}\approx 0.016949153$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{24} by 7x-1.

$$\frac{1}{24}\times 7x+\frac{1}{24}\left(-1\right)=\frac{1}{1.8}\left(0.1-0.2x\right)-\frac{1}{12}\left(5x+1\right)$$

Multiply \frac{1}{24} and 7 to get \frac{7}{24}.

$$\frac{7}{24}x+\frac{1}{24}\left(-1\right)=\frac{1}{1.8}\left(0.1-0.2x\right)-\frac{1}{12}\left(5x+1\right)$$

Multiply \frac{1}{24} and -1 to get -\frac{1}{24}.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{1.8}\left(0.1-0.2x\right)-\frac{1}{12}\left(5x+1\right)$$

Expand \frac{1}{1.8} by multiplying both numerator and the denominator by 10.

$$\frac{7}{24}x-\frac{1}{24}=\frac{10}{18}\left(0.1-0.2x\right)-\frac{1}{12}\left(5x+1\right)$$

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

$$\frac{7}{24}x-\frac{1}{24}=\frac{5}{9}\left(0.1-0.2x\right)-\frac{1}{12}\left(5x+1\right)$$

Use the distributive property to multiply \frac{5}{9} by 0.1-0.2x.

$$\frac{7}{24}x-\frac{1}{24}=\frac{5}{9}\times 0.1+\frac{5}{9}\left(-0.2\right)x-\frac{1}{12}\left(5x+1\right)$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{7}{24}x-\frac{1}{24}=\frac{5}{9}\times \frac{1}{10}+\frac{5}{9}\left(-0.2\right)x-\frac{1}{12}\left(5x+1\right)$$

Multiply \frac{5}{9} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{24}x-\frac{1}{24}=\frac{5\times 1}{9\times 10}+\frac{5}{9}\left(-0.2\right)x-\frac{1}{12}\left(5x+1\right)$$

Do the multiplications in the fraction \frac{5\times 1}{9\times 10}.

$$\frac{7}{24}x-\frac{1}{24}=\frac{5}{90}+\frac{5}{9}\left(-0.2\right)x-\frac{1}{12}\left(5x+1\right)$$

Reduce the fraction \frac{5}{90} to lowest terms by extracting and canceling out 5.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}+\frac{5}{9}\left(-0.2\right)x-\frac{1}{12}\left(5x+1\right)$$

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.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}+\frac{5}{9}\left(-\frac{1}{5}\right)x-\frac{1}{12}\left(5x+1\right)$$

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

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}+\frac{5\left(-1\right)}{9\times 5}x-\frac{1}{12}\left(5x+1\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}+\frac{-1}{9}x-\frac{1}{12}\left(5x+1\right)$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}-\frac{1}{9}x-\frac{1}{12}\left(5x+1\right)$$

Use the distributive property to multiply -\frac{1}{12} by 5x+1.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}-\frac{1}{9}x-\frac{1}{12}\times 5x-\frac{1}{12}$$

Express -\frac{1}{12}\times 5 as a single fraction.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}-\frac{1}{9}x+\frac{-5}{12}x-\frac{1}{12}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}-\frac{1}{9}x-\frac{5}{12}x-\frac{1}{12}$$

Combine -\frac{1}{9}x and -\frac{5}{12}x to get -\frac{19}{36}x.

$$\frac{7}{24}x-\frac{1}{24}=\frac{1}{18}-\frac{19}{36}x-\frac{1}{12}$$

Least common multiple of 18 and 12 is 36. Convert \frac{1}{18} and \frac{1}{12} to fractions with denominator 36.

$$\frac{7}{24}x-\frac{1}{24}=\frac{2}{36}-\frac{19}{36}x-\frac{3}{36}$$

Since \frac{2}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{24}x-\frac{1}{24}=\frac{2-3}{36}-\frac{19}{36}x$$

Subtract 3 from 2 to get -1.

$$\frac{7}{24}x-\frac{1}{24}=-\frac{1}{36}-\frac{19}{36}x$$

Add \frac{19}{36}x to both sides.

$$\frac{7}{24}x-\frac{1}{24}+\frac{19}{36}x=-\frac{1}{36}$$

Combine \frac{7}{24}x and \frac{19}{36}x to get \frac{59}{72}x.

$$\frac{59}{72}x-\frac{1}{24}=-\frac{1}{36}$$

Add \frac{1}{24} to both sides.

$$\frac{59}{72}x=-\frac{1}{36}+\frac{1}{24}$$

Least common multiple of 36 and 24 is 72. Convert -\frac{1}{36} and \frac{1}{24} to fractions with denominator 72.

$$\frac{59}{72}x=-\frac{2}{72}+\frac{3}{72}$$

Since -\frac{2}{72} and \frac{3}{72} have the same denominator, add them by adding their numerators.

$$\frac{59}{72}x=\frac{-2+3}{72}$$

Add -2 and 3 to get 1.

$$\frac{59}{72}x=\frac{1}{72}$$

Multiply both sides by \frac{72}{59}, the reciprocal of \frac{59}{72}.

$$x=\frac{1}{72}\times \frac{72}{59}$$

Multiply \frac{1}{72} times \frac{72}{59} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 72}{72\times 59}$$

Cancel out 72 in both numerator and denominator.

$$x=\frac{1}{59}$$