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

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

Solve for x

$$x = \frac{155}{47} = 3\frac{14}{47} \approx 3.29787234$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by \frac{2}{3}x-2.

$$\frac{1}{5}x+\frac{1}{3}=5\times \frac{2}{3}x-10$$

Express 5\times \frac{2}{3} as a single fraction.

$$\frac{1}{5}x+\frac{1}{3}=\frac{5\times 2}{3}x-10$$

Multiply 5 and 2 to get 10.

$$\frac{1}{5}x+\frac{1}{3}=\frac{10}{3}x-10$$

Subtract \frac{10}{3}x from both sides.

$$\frac{1}{5}x+\frac{1}{3}-\frac{10}{3}x=-10$$

Combine \frac{1}{5}x and -\frac{10}{3}x to get -\frac{47}{15}x.

$$-\frac{47}{15}x+\frac{1}{3}=-10$$

Subtract \frac{1}{3} from both sides.

$$-\frac{47}{15}x=-10-\frac{1}{3}$$

Convert -10 to fraction -\frac{30}{3}.

$$-\frac{47}{15}x=-\frac{30}{3}-\frac{1}{3}$$

Since -\frac{30}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{47}{15}x=\frac{-30-1}{3}$$

Subtract 1 from -30 to get -31.

$$-\frac{47}{15}x=-\frac{31}{3}$$

Multiply both sides by -\frac{15}{47}, the reciprocal of -\frac{47}{15}.

$$x=-\frac{31}{3}\left(-\frac{15}{47}\right)$$

Multiply -\frac{31}{3} times -\frac{15}{47} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-31\left(-15\right)}{3\times 47}$$

Do the multiplications in the fraction \frac{-31\left(-15\right)}{3\times 47}.

$$x=\frac{465}{141}$$

Reduce the fraction \frac{465}{141} to lowest terms by extracting and canceling out 3.

$$x=\frac{155}{47}$$