Solve 4/5(10/3x+5/4)-3/2=-3(frac{3}{2}-x)+frac{20}{3}x

$$\frac { 4 } { 5 } ( \frac { 10 } { 3 } x + \frac { 5 } { 4 } ) - \frac { 3 } { 2 } = - 3 ( \frac { 3 } { 2 } - x ) + \frac { 20 } { 3 } x$$

Solve for x

$$x=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{5} by \frac{10}{3}x+\frac{5}{4}.

$$\frac{4}{5}\times \frac{10}{3}x+\frac{4}{5}\times \frac{5}{4}-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Multiply \frac{4}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 10}{5\times 3}x+\frac{4}{5}\times \frac{5}{4}-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Do the multiplications in the fraction \frac{4\times 10}{5\times 3}.

$$\frac{40}{15}x+\frac{4}{5}\times \frac{5}{4}-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Reduce the fraction \frac{40}{15} to lowest terms by extracting and canceling out 5.

$$\frac{8}{3}x+\frac{4}{5}\times \frac{5}{4}-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Cancel out \frac{4}{5} and its reciprocal \frac{5}{4}.

$$\frac{8}{3}x+1-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{8}{3}x+\frac{2}{2}-\frac{3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}x+\frac{2-3}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

Subtract 3 from 2 to get -1.

$$\frac{8}{3}x-\frac{1}{2}=-3\left(\frac{3}{2}-x\right)+\frac{20}{3}x$$

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

$$\frac{8}{3}x-\frac{1}{2}=-3\times \frac{3}{2}+3x+\frac{20}{3}x$$

Express -3\times \frac{3}{2} as a single fraction.

$$\frac{8}{3}x-\frac{1}{2}=\frac{-3\times 3}{2}+3x+\frac{20}{3}x$$

Multiply -3 and 3 to get -9.

$$\frac{8}{3}x-\frac{1}{2}=\frac{-9}{2}+3x+\frac{20}{3}x$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{8}{3}x-\frac{1}{2}=-\frac{9}{2}+3x+\frac{20}{3}x$$

Combine 3x and \frac{20}{3}x to get \frac{29}{3}x.

$$\frac{8}{3}x-\frac{1}{2}=-\frac{9}{2}+\frac{29}{3}x$$

Subtract \frac{29}{3}x from both sides.

$$\frac{8}{3}x-\frac{1}{2}-\frac{29}{3}x=-\frac{9}{2}$$

Combine \frac{8}{3}x and -\frac{29}{3}x to get -7x.

$$-7x-\frac{1}{2}=-\frac{9}{2}$$

Add \frac{1}{2} to both sides.

$$-7x=-\frac{9}{2}+\frac{1}{2}$$

Since -\frac{9}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-7x=\frac{-9+1}{2}$$

Add -9 and 1 to get -8.

$$-7x=\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$-7x=-4$$

Divide both sides by -7.

$$x=\frac{-4}{-7}$$

Fraction \frac{-4}{-7} can be simplified to \frac{4}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{7}$$