Solve 1/(5x/3-3/4*2/3)=3/8

$$1 / ( \frac { 5 x } { 3 } - \frac { 3 } { 4 } \times \frac { 2 } { 3 } ) = \frac { 3 } { 8 }$$

Solve for x

$$x = \frac{19}{10} = 1\frac{9}{10} = 1.9$$

Steps for Solving Linear Equation

Multiply \frac{3}{4} and \frac{2}{3} to get \frac{1}{2}.

$$\frac{1}{\frac{5x}{3}-\frac{1}{2}}=\frac{3}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{5x}{3} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{3}{3}.

$$\frac{1}{\frac{2\times 5x}{6}-\frac{3}{6}}=\frac{3}{8}$$

Since \frac{2\times 5x}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{2\times 5x-3}{6}}=\frac{3}{8}$$

Do the multiplications in 2\times 5x-3.

$$\frac{1}{\frac{10x-3}{6}}=\frac{3}{8}$$

Divide 1 by \frac{10x-3}{6} by multiplying 1 by the reciprocal of \frac{10x-3}{6}.

$$\frac{6}{10x-3}=\frac{3}{8}$$

Variable x cannot be equal to \frac{3}{10} since division by zero is not defined. Multiply both sides of the equation by 8\left(10x-3\right), the least common multiple of 10x-3,8.

$$8\times 6=3\left(10x-3\right)$$

Multiply 8 and 6 to get 48.

$$48=3\left(10x-3\right)$$

Use the distributive property to multiply 3 by 10x-3.

$$48=30x-9$$

Swap sides so that all variable terms are on the left hand side.

$$30x-9=48$$

Add 9 to both sides.

$$30x=48+9$$

Add 48 and 9 to get 57.

$$30x=57$$

Divide both sides by 30.

$$x=\frac{57}{30}$$

Reduce the fraction \frac{57}{30} to lowest terms by extracting and canceling out 3.

$$x=\frac{19}{10}$$