Solve 3x-1/14=5left(7/10x-4/5right)-6/7x-frac{9}{2}-frac{9}{7}

$$3x- \frac{ 1 }{ 14 } = 5 \left( \frac{ 7 }{ 10 } x- \frac{ 4 }{ 5 } \right) - \frac{ 6 }{ 7 } x- \frac{ 9 }{ 2 } - \frac{ 9 }{ 7 }$$

Solve for x

$$x = -\frac{136}{5} = -27\frac{1}{5} = -27.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by \frac{7}{10}x-\frac{4}{5}.

$$3x-\frac{1}{14}=5\times \frac{7}{10}x+5\left(-\frac{4}{5}\right)-\frac{6}{7}x-\frac{9}{2}-\frac{9}{7}$$

Express 5\times \frac{7}{10} as a single fraction.

$$3x-\frac{1}{14}=\frac{5\times 7}{10}x+5\left(-\frac{4}{5}\right)-\frac{6}{7}x-\frac{9}{2}-\frac{9}{7}$$

Multiply 5 and 7 to get 35.

$$3x-\frac{1}{14}=\frac{35}{10}x+5\left(-\frac{4}{5}\right)-\frac{6}{7}x-\frac{9}{2}-\frac{9}{7}$$

Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$3x-\frac{1}{14}=\frac{7}{2}x+5\left(-\frac{4}{5}\right)-\frac{6}{7}x-\frac{9}{2}-\frac{9}{7}$$

Cancel out 5 and 5.

$$3x-\frac{1}{14}=\frac{7}{2}x-4-\frac{6}{7}x-\frac{9}{2}-\frac{9}{7}$$

Combine \frac{7}{2}x and -\frac{6}{7}x to get \frac{37}{14}x.

$$3x-\frac{1}{14}=\frac{37}{14}x-4-\frac{9}{2}-\frac{9}{7}$$

Convert -4 to fraction -\frac{8}{2}.

$$3x-\frac{1}{14}=\frac{37}{14}x-\frac{8}{2}-\frac{9}{2}-\frac{9}{7}$$

Since -\frac{8}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$3x-\frac{1}{14}=\frac{37}{14}x+\frac{-8-9}{2}-\frac{9}{7}$$

Subtract 9 from -8 to get -17.

$$3x-\frac{1}{14}=\frac{37}{14}x-\frac{17}{2}-\frac{9}{7}$$

Least common multiple of 2 and 7 is 14. Convert -\frac{17}{2} and \frac{9}{7} to fractions with denominator 14.

$$3x-\frac{1}{14}=\frac{37}{14}x-\frac{119}{14}-\frac{18}{14}$$

Since -\frac{119}{14} and \frac{18}{14} have the same denominator, subtract them by subtracting their numerators.

$$3x-\frac{1}{14}=\frac{37}{14}x+\frac{-119-18}{14}$$

Subtract 18 from -119 to get -137.

$$3x-\frac{1}{14}=\frac{37}{14}x-\frac{137}{14}$$

Subtract \frac{37}{14}x from both sides.

$$3x-\frac{1}{14}-\frac{37}{14}x=-\frac{137}{14}$$

Combine 3x and -\frac{37}{14}x to get \frac{5}{14}x.

$$\frac{5}{14}x-\frac{1}{14}=-\frac{137}{14}$$

Add \frac{1}{14} to both sides.

$$\frac{5}{14}x=-\frac{137}{14}+\frac{1}{14}$$

Since -\frac{137}{14} and \frac{1}{14} have the same denominator, add them by adding their numerators.

$$\frac{5}{14}x=\frac{-137+1}{14}$$

Add -137 and 1 to get -136.

$$\frac{5}{14}x=\frac{-136}{14}$$

Reduce the fraction \frac{-136}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{14}x=-\frac{68}{7}$$

Multiply both sides by \frac{14}{5}, the reciprocal of \frac{5}{14}.

$$x=-\frac{68}{7}\times \frac{14}{5}$$

Multiply -\frac{68}{7} times \frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-68\times 14}{7\times 5}$$

Do the multiplications in the fraction \frac{-68\times 14}{7\times 5}.

$$x=\frac{-952}{35}$$

Reduce the fraction \frac{-952}{35} to lowest terms by extracting and canceling out 7.

$$x=-\frac{136}{5}$$