Solve 3/2left(2/3left(1/4x+1right)+2right)-5/2=frac{2}{3}x

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

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

Steps for Solving Linear Equation

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

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

Multiply \frac{2}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 1}{3\times 4}.

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

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

$$\frac{3}{2}\left(\frac{1}{6}x+\frac{2}{3}+2\right)-\frac{5}{2}=\frac{2}{3}x$$

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

$$\frac{3}{2}\left(\frac{1}{6}x+\frac{2}{3}+\frac{6}{3}\right)-\frac{5}{2}=\frac{2}{3}x$$

Since \frac{2}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}\left(\frac{1}{6}x+\frac{2+6}{3}\right)-\frac{5}{2}=\frac{2}{3}x$$

Add 2 and 6 to get 8.

$$\frac{3}{2}\left(\frac{1}{6}x+\frac{8}{3}\right)-\frac{5}{2}=\frac{2}{3}x$$

Use the distributive property to multiply \frac{3}{2} by \frac{1}{6}x+\frac{8}{3}.

$$\frac{3}{2}\times \frac{1}{6}x+\frac{3}{2}\times \frac{8}{3}-\frac{5}{2}=\frac{2}{3}x$$

Multiply \frac{3}{2} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{2\times 6}x+\frac{3}{2}\times \frac{8}{3}-\frac{5}{2}=\frac{2}{3}x$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 6}.

$$\frac{3}{12}x+\frac{3}{2}\times \frac{8}{3}-\frac{5}{2}=\frac{2}{3}x$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}x+\frac{3}{2}\times \frac{8}{3}-\frac{5}{2}=\frac{2}{3}x$$

Multiply \frac{3}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}x+\frac{3\times 8}{2\times 3}-\frac{5}{2}=\frac{2}{3}x$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{4}x+\frac{8}{2}-\frac{5}{2}=\frac{2}{3}x$$

Divide 8 by 2 to get 4.

$$\frac{1}{4}x+4-\frac{5}{2}=\frac{2}{3}x$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{1}{4}x+\frac{8}{2}-\frac{5}{2}=\frac{2}{3}x$$

Since \frac{8}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}x+\frac{8-5}{2}=\frac{2}{3}x$$

Subtract 5 from 8 to get 3.

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

Subtract \frac{2}{3}x from both sides.

$$\frac{1}{4}x+\frac{3}{2}-\frac{2}{3}x=0$$

Combine \frac{1}{4}x and -\frac{2}{3}x to get -\frac{5}{12}x.

$$-\frac{5}{12}x+\frac{3}{2}=0$$

Subtract \frac{3}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{12}x=-\frac{3}{2}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

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

Multiply -\frac{3}{2} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-3\left(-12\right)}{2\times 5}.

$$x=\frac{36}{10}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{18}{5}$$