Solve 3/5x+1/15=7/3(27x-8/35)+frac{7}{5}

$$\frac { 3 } { 5 } x + \frac { 1 } { 15 } = \frac { 7 } { 3 } ( 27 x - \frac { 8 } { 35 } ) + \frac { 7 } { 5 }$$

Solve for x

$$x=-\frac{1}{78}\approx -0.012820513$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{3} by 27x-\frac{8}{35}.

$$\frac{3}{5}x+\frac{1}{15}=\frac{7}{3}\times 27x+\frac{7}{3}\left(-\frac{8}{35}\right)+\frac{7}{5}$$

Express \frac{7}{3}\times 27 as a single fraction.

$$\frac{3}{5}x+\frac{1}{15}=\frac{7\times 27}{3}x+\frac{7}{3}\left(-\frac{8}{35}\right)+\frac{7}{5}$$

Multiply 7 and 27 to get 189.

$$\frac{3}{5}x+\frac{1}{15}=\frac{189}{3}x+\frac{7}{3}\left(-\frac{8}{35}\right)+\frac{7}{5}$$

Divide 189 by 3 to get 63.

$$\frac{3}{5}x+\frac{1}{15}=63x+\frac{7}{3}\left(-\frac{8}{35}\right)+\frac{7}{5}$$

Multiply \frac{7}{3} times -\frac{8}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}x+\frac{1}{15}=63x+\frac{7\left(-8\right)}{3\times 35}+\frac{7}{5}$$

Do the multiplications in the fraction \frac{7\left(-8\right)}{3\times 35}.

$$\frac{3}{5}x+\frac{1}{15}=63x+\frac{-56}{105}+\frac{7}{5}$$

Reduce the fraction \frac{-56}{105} to lowest terms by extracting and canceling out 7.

$$\frac{3}{5}x+\frac{1}{15}=63x-\frac{8}{15}+\frac{7}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{8}{15} and \frac{7}{5} to fractions with denominator 15.

$$\frac{3}{5}x+\frac{1}{15}=63x-\frac{8}{15}+\frac{21}{15}$$

Since -\frac{8}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{3}{5}x+\frac{1}{15}=63x+\frac{-8+21}{15}$$

Add -8 and 21 to get 13.

$$\frac{3}{5}x+\frac{1}{15}=63x+\frac{13}{15}$$

Subtract 63x from both sides.

$$\frac{3}{5}x+\frac{1}{15}-63x=\frac{13}{15}$$

Combine \frac{3}{5}x and -63x to get -\frac{312}{5}x.

$$-\frac{312}{5}x+\frac{1}{15}=\frac{13}{15}$$

Subtract \frac{1}{15} from both sides.

$$-\frac{312}{5}x=\frac{13}{15}-\frac{1}{15}$$

Since \frac{13}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{312}{5}x=\frac{13-1}{15}$$

Subtract 1 from 13 to get 12.

$$-\frac{312}{5}x=\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{312}{5}x=\frac{4}{5}$$

Multiply both sides by -\frac{5}{312}, the reciprocal of -\frac{312}{5}.

$$x=\frac{4}{5}\left(-\frac{5}{312}\right)$$

Multiply \frac{4}{5} times -\frac{5}{312} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{4\left(-5\right)}{5\times 312}$$

Do the multiplications in the fraction \frac{4\left(-5\right)}{5\times 312}.

$$x=\frac{-20}{1560}$$

Reduce the fraction \frac{-20}{1560} to lowest terms by extracting and canceling out 20.

$$x=-\frac{1}{78}$$