Solve 4(1/2x-3/2)-(3/5-x)=4/5x

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

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

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

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

Divide 4 by 2 to get 2.

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

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

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

Multiply 4 and -3 to get -12.

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

Divide -12 by 2 to get -6.

$$2x-6-\left(\frac{3}{5}-x\right)=\frac{4}{5}x$$

To find the opposite of \frac{3}{5}-x, find the opposite of each term.

$$2x-6-\frac{3}{5}-\left(-x\right)=\frac{4}{5}x$$

The opposite of -x is x.

$$2x-6-\frac{3}{5}+x=\frac{4}{5}x$$

Convert -6 to fraction -\frac{30}{5}.

$$2x-\frac{30}{5}-\frac{3}{5}+x=\frac{4}{5}x$$

Since -\frac{30}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$2x+\frac{-30-3}{5}+x=\frac{4}{5}x$$

Subtract 3 from -30 to get -33.

$$2x-\frac{33}{5}+x=\frac{4}{5}x$$

Combine 2x and x to get 3x.

$$3x-\frac{33}{5}=\frac{4}{5}x$$

Subtract \frac{4}{5}x from both sides.

$$3x-\frac{33}{5}-\frac{4}{5}x=0$$

Combine 3x and -\frac{4}{5}x to get \frac{11}{5}x.

$$\frac{11}{5}x-\frac{33}{5}=0$$

Add \frac{33}{5} to both sides. Anything plus zero gives itself.

$$\frac{11}{5}x=\frac{33}{5}$$

Multiply both sides by \frac{5}{11}, the reciprocal of \frac{11}{5}.

$$x=\frac{33}{5}\times \frac{5}{11}$$

Multiply \frac{33}{5} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{33\times 5}{5\times 11}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{33}{11}$$

Divide 33 by 11 to get 3.

$$x=3$$