Solve 1/3x+5/17=14/27x+19/28

$$\frac { 1 } { 3 } x + \frac { 5 } { 17 } = \frac { 14 } { 27 } x + \frac { 19 } { 28 }$$

Solve for x

$$x = -\frac{4941}{2380} = -2\frac{181}{2380} \approx -2.07605042$$

Steps for Solving Linear Equation

Subtract \frac{14}{27}x from both sides.

$$\frac{1}{3}x+\frac{5}{17}-\frac{14}{27}x=\frac{19}{28}$$

Combine \frac{1}{3}x and -\frac{14}{27}x to get -\frac{5}{27}x.

$$-\frac{5}{27}x+\frac{5}{17}=\frac{19}{28}$$

Subtract \frac{5}{17} from both sides.

$$-\frac{5}{27}x=\frac{19}{28}-\frac{5}{17}$$

Least common multiple of 28 and 17 is 476. Convert \frac{19}{28} and \frac{5}{17} to fractions with denominator 476.

$$-\frac{5}{27}x=\frac{323}{476}-\frac{140}{476}$$

Since \frac{323}{476} and \frac{140}{476} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{27}x=\frac{323-140}{476}$$

Subtract 140 from 323 to get 183.

$$-\frac{5}{27}x=\frac{183}{476}$$

Multiply both sides by -\frac{27}{5}, the reciprocal of -\frac{5}{27}.

$$x=\frac{183}{476}\left(-\frac{27}{5}\right)$$

Multiply \frac{183}{476} times -\frac{27}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{183\left(-27\right)}{476\times 5}$$

Do the multiplications in the fraction \frac{183\left(-27\right)}{476\times 5}.

$$x=\frac{-4941}{2380}$$

Fraction \frac{-4941}{2380} can be rewritten as -\frac{4941}{2380} by extracting the negative sign.

$$x=-\frac{4941}{2380}$$