Solve 2/3(3x-6)-1/2(2x-4)=4

$$\frac { 2 } { 3 } ( 3 x - 6 ) - \frac { 1 } { 2 } ( 2 x - 4 ) = 4$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}\times 3x+\frac{2}{3}\left(-6\right)-\frac{1}{2}\left(2x-4\right)=4$$

Cancel out 3 and 3.

$$2x+\frac{2}{3}\left(-6\right)-\frac{1}{2}\left(2x-4\right)=4$$

Express \frac{2}{3}\left(-6\right) as a single fraction.

$$2x+\frac{2\left(-6\right)}{3}-\frac{1}{2}\left(2x-4\right)=4$$

Multiply 2 and -6 to get -12.

$$2x+\frac{-12}{3}-\frac{1}{2}\left(2x-4\right)=4$$

Divide -12 by 3 to get -4.

$$2x-4-\frac{1}{2}\left(2x-4\right)=4$$

Use the distributive property to multiply -\frac{1}{2} by 2x-4.

$$2x-4-\frac{1}{2}\times 2x-\frac{1}{2}\left(-4\right)=4$$

Cancel out 2 and 2.

$$2x-4-x-\frac{1}{2}\left(-4\right)=4$$

Express -\frac{1}{2}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

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

Divide 4 by 2 to get 2.

$$2x-4-x+2=4$$

Combine 2x and -x to get x.

$$x-4+2=4$$

Add -4 and 2 to get -2.

$$x-2=4$$

Add 2 to both sides.

$$x=4+2$$

Add 4 and 2 to get 6.

$$x=6$$