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

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

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and 2 to get 4.

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

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

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

Multiply 2 and -3 to get -6.

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

Divide -6 by 3 to get -2.

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

Subtract 4x from both sides.

$$\frac{4}{3}x-2-4x=0$$

Combine \frac{4}{3}x and -4x to get -\frac{8}{3}x.

$$-\frac{8}{3}x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

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

Multiply both sides by -\frac{3}{8}, the reciprocal of -\frac{8}{3}.

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

Express 2\left(-\frac{3}{8}\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

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