Solve x+2x-6/3--8x+4/2=2x

$$\frac{ x+2x-6 }{ 3 } - \frac{ -8x+4 }{ 2 } = 2x$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(x+2x-6\right)-3\left(-8x+4\right)=12x$$

Combine x and 2x to get 3x.

$$2\left(3x-6\right)-3\left(-8x+4\right)=12x$$

Use the distributive property to multiply 2 by 3x-6.

$$6x-12-3\left(-8x+4\right)=12x$$

Use the distributive property to multiply -3 by -8x+4.

$$6x-12+24x-12=12x$$

Combine 6x and 24x to get 30x.

$$30x-12-12=12x$$

Subtract 12 from -12 to get -24.

$$30x-24=12x$$

Subtract 12x from both sides.

$$30x-24-12x=0$$

Combine 30x and -12x to get 18x.

$$18x-24=0$$

Add 24 to both sides. Anything plus zero gives itself.

$$18x=24$$

Divide both sides by 18.

$$x=\frac{24}{18}$$

Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

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