Solve 4/3+2/3x=41/15+8/5x+frac{4}{5}

$$\frac { 4 } { 3 } + \frac { 2 } { 3 } x = \frac { 41 } { 15 } + \frac { 8 } { 5 } x + \frac { 4 } { 5 }$$

Solve for x

$$x = -\frac{33}{14} = -2\frac{5}{14} \approx -2.357142857$$

Steps for Solving Linear Equation

Least common multiple of 15 and 5 is 15. Convert \frac{41}{15} and \frac{4}{5} to fractions with denominator 15.

$$\frac{4}{3}+\frac{2}{3}x=\frac{41}{15}+\frac{8}{5}x+\frac{12}{15}$$

Since \frac{41}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{2}{3}x=\frac{41+12}{15}+\frac{8}{5}x$$

Add 41 and 12 to get 53.

$$\frac{4}{3}+\frac{2}{3}x=\frac{53}{15}+\frac{8}{5}x$$

Subtract \frac{8}{5}x from both sides.

$$\frac{4}{3}+\frac{2}{3}x-\frac{8}{5}x=\frac{53}{15}$$

Combine \frac{2}{3}x and -\frac{8}{5}x to get -\frac{14}{15}x.

$$\frac{4}{3}-\frac{14}{15}x=\frac{53}{15}$$

Subtract \frac{4}{3} from both sides.

$$-\frac{14}{15}x=\frac{53}{15}-\frac{4}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{53}{15} and \frac{4}{3} to fractions with denominator 15.

$$-\frac{14}{15}x=\frac{53}{15}-\frac{20}{15}$$

Since \frac{53}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{14}{15}x=\frac{53-20}{15}$$

Subtract 20 from 53 to get 33.

$$-\frac{14}{15}x=\frac{33}{15}$$

Reduce the fraction \frac{33}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{14}{15}x=\frac{11}{5}$$

Multiply both sides by -\frac{15}{14}, the reciprocal of -\frac{14}{15}.

$$x=\frac{11}{5}\left(-\frac{15}{14}\right)$$

Multiply \frac{11}{5} times -\frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\left(-15\right)}{5\times 14}$$

Do the multiplications in the fraction \frac{11\left(-15\right)}{5\times 14}.

$$x=\frac{-165}{70}$$

Reduce the fraction \frac{-165}{70} to lowest terms by extracting and canceling out 5.

$$x=-\frac{33}{14}$$