Solve 2/5x-4/3=3/4(16/9x-frac{8}{15}

$$\frac { 2 } { 5 } x - \frac { 4 } { 3 } = \frac { 3 } { 4 } ( \frac { 16 } { 9 } x - \frac { 8 } { 15 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by \frac{16}{9}x-\frac{8}{15}.

$$\frac{2}{5}x-\frac{4}{3}=\frac{3}{4}\times \frac{16}{9}x+\frac{3}{4}\left(-\frac{8}{15}\right)$$

Multiply \frac{3}{4} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}x-\frac{4}{3}=\frac{3\times 16}{4\times 9}x+\frac{3}{4}\left(-\frac{8}{15}\right)$$

Do the multiplications in the fraction \frac{3\times 16}{4\times 9}.

$$\frac{2}{5}x-\frac{4}{3}=\frac{48}{36}x+\frac{3}{4}\left(-\frac{8}{15}\right)$$

Reduce the fraction \frac{48}{36} to lowest terms by extracting and canceling out 12.

$$\frac{2}{5}x-\frac{4}{3}=\frac{4}{3}x+\frac{3}{4}\left(-\frac{8}{15}\right)$$

Multiply \frac{3}{4} times -\frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}x-\frac{4}{3}=\frac{4}{3}x+\frac{3\left(-8\right)}{4\times 15}$$

Do the multiplications in the fraction \frac{3\left(-8\right)}{4\times 15}.

$$\frac{2}{5}x-\frac{4}{3}=\frac{4}{3}x+\frac{-24}{60}$$

Reduce the fraction \frac{-24}{60} to lowest terms by extracting and canceling out 12.

$$\frac{2}{5}x-\frac{4}{3}=\frac{4}{3}x-\frac{2}{5}$$

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

$$\frac{2}{5}x-\frac{4}{3}-\frac{4}{3}x=-\frac{2}{5}$$

Combine \frac{2}{5}x and -\frac{4}{3}x to get -\frac{14}{15}x.

$$-\frac{14}{15}x-\frac{4}{3}=-\frac{2}{5}$$

Add \frac{4}{3} to both sides.

$$-\frac{14}{15}x=-\frac{2}{5}+\frac{4}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{2}{5} and \frac{4}{3} to fractions with denominator 15.

$$-\frac{14}{15}x=-\frac{6}{15}+\frac{20}{15}$$

Since -\frac{6}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$-\frac{14}{15}x=\frac{-6+20}{15}$$

Add -6 and 20 to get 14.

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

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

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

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

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

Cancel out 14 in both numerator and denominator.

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

Divide -15 by 15 to get -1.

$$x=-1$$