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

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

Solve for x

$$x=\frac{15}{16}=0.9375$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 4,3,2,5.

$$45\times 2\times \frac{1}{3}-100\left(x-\frac{3}{2}\right)=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Multiply 45 and 2 to get 90.

$$90\times \frac{1}{3}-100\left(x-\frac{3}{2}\right)=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Multiply 90 and \frac{1}{3} to get \frac{90}{3}.

$$\frac{90}{3}-100\left(x-\frac{3}{2}\right)=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Divide 90 by 3 to get 30.

$$30-100\left(x-\frac{3}{2}\right)=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Use the distributive property to multiply -100 by x-\frac{3}{2}.

$$30-100x-100\left(-\frac{3}{2}\right)=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Express -100\left(-\frac{3}{2}\right) as a single fraction.

$$30-100x+\frac{-100\left(-3\right)}{2}=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Multiply -100 and -3 to get 300.

$$30-100x+\frac{300}{2}=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Divide 300 by 2 to get 150.

$$30-100x+150=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Add 30 and 150 to get 180.

$$180-100x=36\left(1-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Use the distributive property to multiply 36 by 1-\frac{2x}{5}.

$$180-100x=36+36\left(-\frac{2x}{5}\right)-30\left(2x-4\right)$$

Express 36\left(-\frac{2x}{5}\right) as a single fraction.

$$180-100x=36+\frac{-36\times 2x}{5}-30\left(2x-4\right)$$

Multiply -36 and 2 to get -72.

$$180-100x=36+\frac{-72x}{5}-30\left(2x-4\right)$$

Use the distributive property to multiply -30 by 2x-4.

$$180-100x=36+\frac{-72x}{5}-60x+120$$

Add 36 and 120 to get 156.

$$180-100x=156+\frac{-72x}{5}-60x$$

Subtract \frac{-72x}{5} from both sides.

$$180-100x-\frac{-72x}{5}=156-60x$$

Add 60x to both sides.

$$180-100x-\frac{-72x}{5}+60x=156$$

Combine -100x and 60x to get -40x.

$$180-40x-\frac{-72x}{5}=156$$

Subtract 180 from both sides.

$$-40x-\frac{-72x}{5}=156-180$$

Subtract 180 from 156 to get -24.

$$-40x-\frac{-72x}{5}=-24$$

Multiply both sides of the equation by 5.

$$-200x+72x=-120$$

Combine -200x and 72x to get -128x.

$$-128x=-120$$

Divide both sides by -128.

$$x=\frac{-120}{-128}$$

Reduce the fraction \frac{-120}{-128} to lowest terms by extracting and canceling out -8.

$$x=\frac{15}{16}$$