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

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

Solve for x

$$x = \frac{34}{33} = 1\frac{1}{33} \approx 1.03030303$$

Steps for Solving Linear Equation

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

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

Cancel out 3 and 3.

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

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

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

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

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

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

$$3x-2=\frac{4}{5}x+\frac{4}{15}$$

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

$$3x-2-\frac{4}{5}x=\frac{4}{15}$$

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

$$\frac{11}{5}x-2=\frac{4}{15}$$

Add 2 to both sides.

$$\frac{11}{5}x=\frac{4}{15}+2$$

Convert 2 to fraction \frac{30}{15}.

$$\frac{11}{5}x=\frac{4}{15}+\frac{30}{15}$$

Since \frac{4}{15} and \frac{30}{15} have the same denominator, add them by adding their numerators.

$$\frac{11}{5}x=\frac{4+30}{15}$$

Add 4 and 30 to get 34.

$$\frac{11}{5}x=\frac{34}{15}$$

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

$$x=\frac{34}{15}\times \frac{5}{11}$$

Multiply \frac{34}{15} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{34\times 5}{15\times 11}$$

Do the multiplications in the fraction \frac{34\times 5}{15\times 11}.

$$x=\frac{170}{165}$$

Reduce the fraction \frac{170}{165} to lowest terms by extracting and canceling out 5.

$$x=\frac{34}{33}$$