Solve 3/4[4/5[2/3(1/2x-4)-2]+4]-9=0

$$\frac { 3 } { 4 } [ \frac { 4 } { 5 } [ \frac { 2 } { 3 } ( \frac { 1 } { 2 } x - 4 ) - 2 ] + 4 ] - 9 = 0$$

Solve for x

$$x=44$$

Steps for Solving Linear Equation

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

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{2}{3}\times \frac{1}{2}x+\frac{2}{3}\left(-4\right)-2\right)+4\right)-9=0$$

Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{2\times 1}{3\times 2}x+\frac{2}{3}\left(-4\right)-2\right)+4\right)-9=0$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x+\frac{2}{3}\left(-4\right)-2\right)+4\right)-9=0$$

Express \frac{2}{3}\left(-4\right) as a single fraction.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x+\frac{2\left(-4\right)}{3}-2\right)+4\right)-9=0$$

Multiply 2 and -4 to get -8.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x+\frac{-8}{3}-2\right)+4\right)-9=0$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x-\frac{8}{3}-2\right)+4\right)-9=0$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x-\frac{8}{3}-\frac{6}{3}\right)+4\right)-9=0$$

Since -\frac{8}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x+\frac{-8-6}{3}\right)+4\right)-9=0$$

Subtract 6 from -8 to get -14.

$$\frac{3}{4}\left(\frac{4}{5}\left(\frac{1}{3}x-\frac{14}{3}\right)+4\right)-9=0$$

Use the distributive property to multiply \frac{4}{5} by \frac{1}{3}x-\frac{14}{3}.

$$\frac{3}{4}\left(\frac{4}{5}\times \frac{1}{3}x+\frac{4}{5}\left(-\frac{14}{3}\right)+4\right)-9=0$$

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

$$\frac{3}{4}\left(\frac{4\times 1}{5\times 3}x+\frac{4}{5}\left(-\frac{14}{3}\right)+4\right)-9=0$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 3}.

$$\frac{3}{4}\left(\frac{4}{15}x+\frac{4}{5}\left(-\frac{14}{3}\right)+4\right)-9=0$$

Multiply \frac{4}{5} times -\frac{14}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}\left(\frac{4}{15}x+\frac{4\left(-14\right)}{5\times 3}+4\right)-9=0$$

Do the multiplications in the fraction \frac{4\left(-14\right)}{5\times 3}.

$$\frac{3}{4}\left(\frac{4}{15}x+\frac{-56}{15}+4\right)-9=0$$

Fraction \frac{-56}{15} can be rewritten as -\frac{56}{15} by extracting the negative sign.

$$\frac{3}{4}\left(\frac{4}{15}x-\frac{56}{15}+4\right)-9=0$$

Convert 4 to fraction \frac{60}{15}.

$$\frac{3}{4}\left(\frac{4}{15}x-\frac{56}{15}+\frac{60}{15}\right)-9=0$$

Since -\frac{56}{15} and \frac{60}{15} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\left(\frac{4}{15}x+\frac{-56+60}{15}\right)-9=0$$

Add -56 and 60 to get 4.

$$\frac{3}{4}\left(\frac{4}{15}x+\frac{4}{15}\right)-9=0$$

Use the distributive property to multiply \frac{3}{4} by \frac{4}{15}x+\frac{4}{15}.

$$\frac{3}{4}\times \frac{4}{15}x+\frac{3}{4}\times \frac{4}{15}-9=0$$

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

$$\frac{3\times 4}{4\times 15}x+\frac{3}{4}\times \frac{4}{15}-9=0$$

Cancel out 4 in both numerator and denominator.

$$\frac{3}{15}x+\frac{3}{4}\times \frac{4}{15}-9=0$$

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

$$\frac{1}{5}x+\frac{3}{4}\times \frac{4}{15}-9=0$$

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

$$\frac{1}{5}x+\frac{3\times 4}{4\times 15}-9=0$$

Cancel out 4 in both numerator and denominator.

$$\frac{1}{5}x+\frac{3}{15}-9=0$$

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

$$\frac{1}{5}x+\frac{1}{5}-9=0$$

Convert 9 to fraction \frac{45}{5}.

$$\frac{1}{5}x+\frac{1}{5}-\frac{45}{5}=0$$

Since \frac{1}{5} and \frac{45}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}x+\frac{1-45}{5}=0$$

Subtract 45 from 1 to get -44.

$$\frac{1}{5}x-\frac{44}{5}=0$$

Add \frac{44}{5} to both sides. Anything plus zero gives itself.

$$\frac{1}{5}x=\frac{44}{5}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x=\frac{44}{5}\times 5$$

Cancel out 5 and 5.

$$x=44$$