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

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

Solve for x

$$x=\frac{6}{17}\approx 0.352941176$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 3 and -2 to get -6.

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

Divide -6 by 2 to get -3.

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

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

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

Combine 4x and 6x to get 10x.

$$\frac{3}{2}x-3=10x-6$$

Subtract 10x from both sides.

$$\frac{3}{2}x-3-10x=-6$$

Combine \frac{3}{2}x and -10x to get -\frac{17}{2}x.

$$-\frac{17}{2}x-3=-6$$

Add 3 to both sides.

$$-\frac{17}{2}x=-6+3$$

Add -6 and 3 to get -3.

$$-\frac{17}{2}x=-3$$

Multiply both sides by -\frac{2}{17}, the reciprocal of -\frac{17}{2}.

$$x=-3\left(-\frac{2}{17}\right)$$

Express -3\left(-\frac{2}{17}\right) as a single fraction.

$$x=\frac{-3\left(-2\right)}{17}$$

Multiply -3 and -2 to get 6.

$$x=\frac{6}{17}$$