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

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

Solve for x

$$x=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Subtract 4x from both sides.

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

Combine \frac{2}{3}x and -4x to get -\frac{10}{3}x.

$$-\frac{10}{3}x-\frac{4}{3}=0$$

Add \frac{4}{3} to both sides. Anything plus zero gives itself.

$$-\frac{10}{3}x=\frac{4}{3}$$

Multiply both sides by -\frac{3}{10}, the reciprocal of -\frac{10}{3}.

$$x=\frac{4}{3}\left(-\frac{3}{10}\right)$$

Multiply \frac{4}{3} times -\frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{4\left(-3\right)}{3\times 10}$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{3\times 10}.

$$x=\frac{-12}{30}$$

Reduce the fraction \frac{-12}{30} to lowest terms by extracting and canceling out 6.

$$x=-\frac{2}{5}$$