Solve 3/19*(-6/1x+4/1)=1/5*(frac{2}{1}x+frac{5}{10})

$$\frac { 3 } { 19 } \cdot ( \frac { - 6 } { 1 } x + \frac { 4 } { 1 } ) = \frac { 1 } { 5 } \cdot ( \frac { 2 } { 1 } x + \frac { 5 } { 10 } )$$

Solve for x

$$x=\frac{101}{256}=0.39453125$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\frac{3}{19}\left(-6x+\frac{4}{1}\right)=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Anything divided by one gives itself.

$$\frac{3}{19}\left(-6x+4\right)=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Use the distributive property to multiply \frac{3}{19} by -6x+4.

$$\frac{3}{19}\left(-6\right)x+\frac{3}{19}\times 4=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Express \frac{3}{19}\left(-6\right) as a single fraction.

$$\frac{3\left(-6\right)}{19}x+\frac{3}{19}\times 4=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Multiply 3 and -6 to get -18.

$$\frac{-18}{19}x+\frac{3}{19}\times 4=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Fraction \frac{-18}{19} can be rewritten as -\frac{18}{19} by extracting the negative sign.

$$-\frac{18}{19}x+\frac{3}{19}\times 4=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Express \frac{3}{19}\times 4 as a single fraction.

$$-\frac{18}{19}x+\frac{3\times 4}{19}=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Multiply 3 and 4 to get 12.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{1}{5}\left(\frac{2}{1}x+\frac{5}{10}\right)$$

Anything divided by one gives itself.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{1}{5}\left(2x+\frac{5}{10}\right)$$

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

$$-\frac{18}{19}x+\frac{12}{19}=\frac{1}{5}\left(2x+\frac{1}{2}\right)$$

Use the distributive property to multiply \frac{1}{5} by 2x+\frac{1}{2}.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{1}{5}\times 2x+\frac{1}{5}\times \frac{1}{2}$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{2}{5}x+\frac{1}{5}\times \frac{1}{2}$$

Multiply \frac{1}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{2}{5}x+\frac{1\times 1}{5\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 2}.

$$-\frac{18}{19}x+\frac{12}{19}=\frac{2}{5}x+\frac{1}{10}$$

Subtract \frac{2}{5}x from both sides.

$$-\frac{18}{19}x+\frac{12}{19}-\frac{2}{5}x=\frac{1}{10}$$

Combine -\frac{18}{19}x and -\frac{2}{5}x to get -\frac{128}{95}x.

$$-\frac{128}{95}x+\frac{12}{19}=\frac{1}{10}$$

Subtract \frac{12}{19} from both sides.

$$-\frac{128}{95}x=\frac{1}{10}-\frac{12}{19}$$

Least common multiple of 10 and 19 is 190. Convert \frac{1}{10} and \frac{12}{19} to fractions with denominator 190.

$$-\frac{128}{95}x=\frac{19}{190}-\frac{120}{190}$$

Since \frac{19}{190} and \frac{120}{190} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{128}{95}x=\frac{19-120}{190}$$

Subtract 120 from 19 to get -101.

$$-\frac{128}{95}x=-\frac{101}{190}$$

Multiply both sides by -\frac{95}{128}, the reciprocal of -\frac{128}{95}.

$$x=-\frac{101}{190}\left(-\frac{95}{128}\right)$$

Multiply -\frac{101}{190} times -\frac{95}{128} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-101\left(-95\right)}{190\times 128}$$

Do the multiplications in the fraction \frac{-101\left(-95\right)}{190\times 128}.

$$x=\frac{9595}{24320}$$

Reduce the fraction \frac{9595}{24320} to lowest terms by extracting and canceling out 95.

$$x=\frac{101}{256}$$