Solve 2/3(x+6)=2x

$$\frac { 2 } { 3 } ( x + 6 ) = 2 x$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x+6.

$$\frac{2}{3}x+\frac{2}{3}\times 6=2x$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{2}{3}x+\frac{2\times 6}{3}=2x$$

Multiply 2 and 6 to get 12.

$$\frac{2}{3}x+\frac{12}{3}=2x$$

Divide 12 by 3 to get 4.

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

Subtract 2x from both sides.

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

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

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

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides by -\frac{3}{4}, the reciprocal of -\frac{4}{3}.

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

Multiply -4 times -\frac{3}{4}.

$$x=3$$