Solve 4/5[5/4(2/3x-1/3)-5]=-frac{4}{3}x-frac{1}{3}

$$\frac { 4 } { 5 } [ \frac { 5 } { 4 } ( \frac { 2 } { 3 } x - \frac { 1 } { 3 } ) - 5 ] = - \frac { 4 } { 3 } x - \frac { 1 } { 3 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{4} by \frac{2}{3}x-\frac{1}{3}.

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

Multiply \frac{5}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 2}{4\times 3}.

$$\frac{4}{5}\left(\frac{10}{12}x+\frac{5}{4}\left(-\frac{1}{3}\right)-5\right)=-\frac{4}{3}x-\frac{1}{3}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{5}{4} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\left(-1\right)}{4\times 3}.

$$\frac{4}{5}\left(\frac{5}{6}x+\frac{-5}{12}-5\right)=-\frac{4}{3}x-\frac{1}{3}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$\frac{4}{5}\left(\frac{5}{6}x-\frac{5}{12}-5\right)=-\frac{4}{3}x-\frac{1}{3}$$

Convert 5 to fraction \frac{60}{12}.

$$\frac{4}{5}\left(\frac{5}{6}x-\frac{5}{12}-\frac{60}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Since -\frac{5}{12} and \frac{60}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}\left(\frac{5}{6}x+\frac{-5-60}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Subtract 60 from -5 to get -65.

$$\frac{4}{5}\left(\frac{5}{6}x-\frac{65}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Use the distributive property to multiply \frac{4}{5} by \frac{5}{6}x-\frac{65}{12}.

$$\frac{4}{5}\times \frac{5}{6}x+\frac{4}{5}\left(-\frac{65}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Multiply \frac{4}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{5\times 6}x+\frac{4}{5}\left(-\frac{65}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{6}x+\frac{4}{5}\left(-\frac{65}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x+\frac{4}{5}\left(-\frac{65}{12}\right)=-\frac{4}{3}x-\frac{1}{3}$$

Multiply \frac{4}{5} times -\frac{65}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x+\frac{4\left(-65\right)}{5\times 12}=-\frac{4}{3}x-\frac{1}{3}$$

Do the multiplications in the fraction \frac{4\left(-65\right)}{5\times 12}.

$$\frac{2}{3}x+\frac{-260}{60}=-\frac{4}{3}x-\frac{1}{3}$$

Reduce the fraction \frac{-260}{60} to lowest terms by extracting and canceling out 20.

$$\frac{2}{3}x-\frac{13}{3}=-\frac{4}{3}x-\frac{1}{3}$$

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

$$\frac{2}{3}x-\frac{13}{3}+\frac{4}{3}x=-\frac{1}{3}$$

Combine \frac{2}{3}x and \frac{4}{3}x to get 2x.

$$2x-\frac{13}{3}=-\frac{1}{3}$$

Add \frac{13}{3} to both sides.

$$2x=-\frac{1}{3}+\frac{13}{3}$$

Since -\frac{1}{3} and \frac{13}{3} have the same denominator, add them by adding their numerators.

$$2x=\frac{-1+13}{3}$$

Add -1 and 13 to get 12.

$$2x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$