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

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

Solve for x

$$x = \frac{179}{5} = 35\frac{4}{5} = 35.8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by \frac{7}{10}x-\frac{1}{5}.

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

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

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

Multiply 5 and 7 to get 35.

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

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

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

Cancel out 5 and 5.

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

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

$$3x-14=\frac{37}{14}x-1-\left(\frac{3}{2}-\frac{9}{7}\right)$$

Least common multiple of 2 and 7 is 14. Convert \frac{3}{2} and \frac{9}{7} to fractions with denominator 14.

$$3x-14=\frac{37}{14}x-1-\left(\frac{21}{14}-\frac{18}{14}\right)$$

Since \frac{21}{14} and \frac{18}{14} have the same denominator, subtract them by subtracting their numerators.

$$3x-14=\frac{37}{14}x-1-\frac{21-18}{14}$$

Subtract 18 from 21 to get 3.

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

Convert -1 to fraction -\frac{14}{14}.

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

Since -\frac{14}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -14 to get -17.

$$3x-14=\frac{37}{14}x-\frac{17}{14}$$

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

$$3x-14-\frac{37}{14}x=-\frac{17}{14}$$

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

$$\frac{5}{14}x-14=-\frac{17}{14}$$

Add 14 to both sides.

$$\frac{5}{14}x=-\frac{17}{14}+14$$

Convert 14 to fraction \frac{196}{14}.

$$\frac{5}{14}x=-\frac{17}{14}+\frac{196}{14}$$

Since -\frac{17}{14} and \frac{196}{14} have the same denominator, add them by adding their numerators.

$$\frac{5}{14}x=\frac{-17+196}{14}$$

Add -17 and 196 to get 179.

$$\frac{5}{14}x=\frac{179}{14}$$

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

$$x=\frac{179}{14}\times \frac{14}{5}$$

Multiply \frac{179}{14} times \frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{179\times 14}{14\times 5}$$

Cancel out 14 in both numerator and denominator.

$$x=\frac{179}{5}$$